Rotating a graph like this requires trigonometry. attempted to draw here in yellow is a parabola, and as we've already No matter what you're writing, good writing is always about engaging your audience and communicating your message clearly. Square Root Function Inverse of a parabola. WebThe length of the latera recta (focal width) is \frac {2 b^ {2}} {a} = \frac {8} {3} a2b2 = 38. Now let's see if we can simplify things. If we consider only parabolas that open upwards or downwards, then the directrix will be a horizontal line of the form y = c . Direct link to camerongeller's post at 2:45 shouldn't it be (, Posted 8 years ago. 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It only takes a few minutes. point right over here, and its x-coordinate is x, It moves the node in a circle around a pivot point. {eq}\begin{align*} 4p & =-8\\ p & = \frac {-8}{4}\\ \mathbf{p} & = \mathbf{-2}\\ \end{align*} {/eq}. Basic. Drive Student Mastery. WebFind Equation of Parabola given Focus and Directrix 7.2. distance to the directrix, we literally just drop a perpendicular, I guess you could say say, that is, that's going to be the shortest distance to that line, but the distance to the focus, well we see that's at a bit of an angle, and we might have to use Furthermore, the Directrix of a parabola can also be calculated by a simple equation that is: y = c \frac { (b + 1)} { (4a)} . How Parabola Calculator Works? Parabola equation calculator makes the calculation faster and error-free as it uses the maths parabola equation. To get convenience, you need to follow these steps: Pict History, Kingdoms & Language | Who were the Picts of Peasants: History & Facts | What is Peasantry? Direct link to James Wu's post I guess it could, if the , Posted 8 years ago. WebEquation of a parabola given focus and directrix calculator Take any parabola equation, and find a, b, c values from equation substitute those values in Vertex v(h, k). Webparabola generator: vertex, focus, directrix. Well, we can evaluate the axis of symmetry, focus, directrix, vertex, x intercept, y intercept by using the parabola formula in the form of \( x = y^2 + bx + c \). The process of obtaining the equation is similar, but it is more algebraically intensive. Use this user friendly Parabola Calculator tool to get the output in a short span of time. That is true for the left hand side, but on the right hand side, it's not quite the same. Equations. - Definition, History, Types & Magnification: Definition, Formula, Calculation & Examples. Direct link to The_perfect_apology's post At 3:26 why does Sal squa, Posted 7 years ago. WebThe parabola calculator finds the vertex form, focus and directrix of every parabola. The parabola has many important applications, from a parabolic microphone or parabolic antenna to automobile headlight reflectors and the design of ballistic missiles. on the left-hand side, so, plus 2yb, that's gonna give us a In the same way, you can translate the parabola horizontally. WebIn order to find the focus of a parabola, you must know that the equation of a parabola in a vertex form is y=a(x-h)2+k where a represents the 606 Experts 94% Recurring customers This parabola is of the form {eq}{(x-h)}^2=4p(y-k) {/eq} so it opens vertically. Anyways, can it teach me to be math genius?. squared from both sides, so, subtract k squared from both sides, so that's gonna get rid of So let's take a arbitrary Watch later. When it gives you an answer it tells what formulas you have to use to solve the problem, the person that made and came up with this idea is an angel. h = b ( 2a), k = c b2 ( 4a). Focus and Directrix of Parabola. WebFind Equation of Parabola given Focus and Directrix 7.2 parabola equation solver, calculator from points, calculator, graphing vertex, standard of a hyperbola focus and directrix. substitute those values in Vertex \( v(h,k) \). The focus of the is parabola {eq}\mathbf{(8,2)} {/eq} and the directrix is {eq}\mathbf{x = 2} {/eq}. That's going to be-- Actually, let me start Clear up math equations If you're struggling to clear up a math problem, don't give up! Feel free to contact us at your convenience! Looking for a fast solution? {eq}\begin{align*} y & =-1-(-2)\\ y & =-1+2= 1\\ \end{align*} {/eq}. The second directrix is x = h + \frac {a^ {2}} {c} = \frac {9 \sqrt {5}} {5} x = h + ca2 = 59 5. To find the equation of the parabola. A parabola is the shape of the graph of a quadratic. WebFind equation of parabola given focus and directrix calculator. Work up its side it becomes y = x or mathematically expressed as y = x. These people know what you need for math! Finding The Focus and Directrix of a Parabola - Conic Sections Share Watch on Write the equation of the parabola Given the directrix y = 2 and focus (0, 8) find: The vertex. So please try to do so. For an Real World Applications. focus vertex directrix. To get convenience, you need to follow these steps: The Parabola equation calculator computes: Whenever the distance between the focus and parabola directrix increases, |a| will decrease. Vertex of a Parabola. It means that the parabola gets widen with the increase of distance among its two parameters. Since the directrix is vertical, use the equation of a parabola that opens up or down. Find the vertex. How to Find a Parabola's Equation from Its Directrix and Focus The first directrix is x = h - \frac {a^ {2}} {c} = - \frac {9 \sqrt {5}} {5} x = h ca2 = 59 5. It's going to be this y, minus k. It's just this distance. The distinct difference is that they are generated through different methods. 2yb on the left-hand side, plus 2yb. Direct link to Raseen's post What if the equation of a, Posted 8 years ago. focus (x,y) = (_____) directrix = focal diameter = This problem has been solved! (x-a)2+b2-c2=2(b-c)y. Parabola equation calculator makes the calculation faster and error-free as it uses the maths parabola equation. They are frequently used in engineering, physics and other areas. distance to the directrix, which I'm drawing here in blue, has to be the same as the Parabola: A parabola is a curved shape where any point is at an equal distance from a fixed point, and a fixed straight line. However, an Online Hyperbola Calculator will help you to determine the center, eccentricity, focal parameter, major, and asymptote for given values in the hyperbola equation. For quick and easy calculations, you can use an online parabola grapher that plots the graphical representation of the given parabola equation. The parabolas focus is easily found via, say, a vector computation: The vertex is midway between the focus and directrix. Step 2 Find the vertex. Now, I said all I want is (x-a)2+b2-c2=2(b-c)y. Find equation of parabola given focus and directrix calculator - 25023402. by two times, b minus k. So, let's divide everything, two times, b minus k, so, two times, b minus k. And I'm actually gonna It's not (b-k)^2 its b^2 - k^2 gives (b+k)(b-k). WebGiven the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)^2 / (m^2 +1) = (x - h)^2 + (y - k)^2. sitting on the parabola, that distance needs to be Additionally, the parabola grapher displays the graph for the given equation. Substitution Techniques for Difficult Integrals, Blood Clot in the Arm: Symptoms, Signs & Treatment. Write the equation of the parabola Given the directrix y = 2 and focus (0, 8) find: The vertex. The way I've just drawn it, yes, y is greater than k, so this is going to give WebParabola Calculator Well, we can evaluate the axis of symmetry, focus, directrix, vertex, x intercept, y intercept by using the parabola formula in the form of x = y 2 + b x + c . So it's going to be y minus k. Now we have to be careful. Learn how to write the equation of a parabola given the focus and the directrix. Can cylindrical mirror/catoptric drawing be related to directrix and focus intuition of parabolas? These things cancel out. Create your account. Direct link to Daniel's post At 7:34, what happened to, Posted 7 years ago. Step 1. Info. We can find the x intercept, y intercept, vertex, focus, directrix, axis of symmetry using any parabola equation in the form of y Directrix: x=, Vertex: The vertex (h,k) ( h , k ) of a parabola is the midpoint between the focus and directrix. By checking the below sections, you will get a good knowledge on the parabola equation concept and you will also obtain a handy calculator tool that gives result in fraction of seconds. Get unlimited access to over 88,000 lessons. Rarely Tested Question Types - Conjunctions: Study.com What is IV Therapy? bit of hairy algebra, but it really is not too bad. Given Parabola equation is y = 5x2+ 4x + 10, The standard form of the equation is y = ax2+ bx + c, The parabola equation in vertex form is y = a(x-h)2+ k, The focus of x coordinate = -b/ 2a = -2/5, Focus of y coordinate is = c (b2 1)/ (4a), Directrix equation y = c (b2+ 1) / (4a), To get y-intercept put x = 0 in the equation, To get x-intercept put y = 0 in the equation. WebFinding the Equation of a Parabola Given Focus and focus vertex directrix. Now just Plot the points and sketch your parabola graph. delivering on that promise. A fixed straight line is known as the parabola directrix. It takes two equations: its the same thing. WebThis calculator will find either the equation of the parabola from the given parameters or the vertex, focus, directrix, axis of symmetry, latus rectum Decide math questions Thanks to the great satisfaction rating, I will definitely be using this product again! I find it great how it explains each solution, it has its problems, but an app THIS is good is bound to, I love this app so much, I have only had 1 real problem with this app, the problem is when I'm using scienctific notation and I need to convert a number to scienctific notation but it's " ### x 10. Determine math question In order to determine what the math problem is, you will It lets you understand how to put the values in the parabola formula as well. Calculate parabola directrix given equation step-by-step. Therefore, 4a = 24. a = 24/4 = 6. An error occurred trying to load this video. We use the equation x=h-p x = h - p to find the directrix. PS: If you want your problem to load that easily, use the wifi! WebFinding the Equation of a Parabola Given Focus and. Answers in 3 seconds is a great resource for quick, reliable answers to all of your questions. Shopping. If you need your order delivered immediately, we can accommodate your request. Let P (x, y) be any point on the parabola whose focus S (x1, y1) and the directrix is the straight line ax + by + c =0. You can get math help online by visiting websites like Khan Academy or Mathway. All those calculations that involve parabola can be made easy by using a parabola calculator. Helps me out a ton. Tap for more steps x y 2 1 1 1 4 0 0 1 1 4 2 1 x y - 2 1 - 1 1 4 0 0 1 1 4 2 1 Consider, for example, the parabola whose focus is at, Therefore, the equation of the parabola with focus (a,b) and directrix y=c is. Question 2: Find the equation, focus, axis of symmetry, vertex, directrix, focal parameter, x-intercepts, y-intercepts of the parabola that passes through the points (1,4), (2,9), (1,6)? Mathematics is the science of numbers, equations, and shapes. Experts will give you an answer in real-time, How to find the exact value of a trigonometric function sin, How to find the rule of a sequence calculator, How to find the vertical asymptote of a function using limits, How to solve simple equations with 2 variables, Measure the radius and diameter of the following circles, Multiplying and dividing radicals calculator, Solving multi linear equations with absolute value, Solving systems of equations by substitution and elimination worksheets with answers. Direct link to jwinder47's post The reason is because the, Posted 7 years ago. copyright 2003-2023 Study.com. WebThis calculator will find either the equation of the parabola from the given parameters or the vertex, focus, directrix, axis of symmetry, latus rectum Homework Support Online So, I have a y squared on the left, I have a y squared on the right, well, if I subtract y Cancel any time. WebFind the Parabola with Focus (2,0) and Directrix x=-2 (2,0) x=-2 Step 1 Since the directrixis horizontal, use the equationof a parabolathat opens left or right. So, this tool always ready to provide its services to everyone in the blink of an eye and without any cost. It can serve as the following: 4, 4a, 4b parable table focus vertex ex: Y = x 2 4 x + 5. order now Send feedback | Visit Wolfram|Alpha. It is a widget where you type the focus and the vertex of the parabola and it shows the equation and properties of it. Step 2: Find {eq}h, k {/eq}, and {eq}p {/eq} using the equation of the parabola {eq}{(x-h)}^2=4p(y-k) {/eq} or {eq}{(y-k)}^2=4p(x-h) {/eq}. WebThe parabola equation calculator displays the graph of the parabola after entering the required values. WebIn order to find the focus of a parabola, you must know that the equation of a parabola in a vertex form is y=a(x-h)2+k where a represents the 606 Experts 94% Recurring customers Step 2: Find {eq}h, k {/eq}, and {eq}p {/eq} by comparing the given equation with the standard equation of the parabola. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. If you're looking for a reliable support system, you can trust us. Find the Parabola with Focus (1,2) and Directrix y=-2 (1,2) y=-2 Step 1 Since the directrixis vertical, use the equationof a parabolathat opens up or down. X coordinate. However, for manual plotting of parabola graph you have to follow some steps: The first type of transformation is known as Translation. How to Solve the Parabola Equation? Output: equation of parabola is 4.0 x^2 + 1.0 y^2 + 4.0 x + 32.0 y + 4.0 xy + 16.0 = 0. Webparabola equation solver, calculator from points, calculator, graphing vertex, standard of a hyperbola focus and directrix. Call the focus coordinates (P, Q) and the directrix line Y = R. Step 2. It is used to solve problems in a variety of fields, including science, engineering, and business. Along with all these mathematical values, this parabola grapher displays the graph of the parabola in the end. How do you graph lines in slope intercept form, How to find the sum of n terms in a geometric series, How to get volume in straight hair overnight, Interview questions and answers in english, Methods to calculate elasticity of demand. Check out our extensive collection of tips and tricks designed to help you get the most out of your day. Fair enough? Now, the selected equation for the parabola will be displayed. If yes, this is the right spot for you. Mathematics is the study of numbers, patterns, and relationships. Formula for focus: If the parabola is of the form {eq}{(x-h)}^2=4p(y-k) {/eq} then the formula for the focus is: If the parabola is of the form {eq}{(y-k)}^2=4p(x-h) {/eq} then the formula for the focus is: $$\mathbf{(h + p, k)} $$, Equation for directrix: If the parabola is of the form {eq}{(x-h)}^2=4p(y-k) {/eq} then the equation for the directrix is: $$\mathbf{y=k-p} $$, If the parabola is of the form {eq}{(y-k)}^2=4p(x-h) {/eq} then the equations for the directrix is: $$\mathbf{x = h - p} $$. On the right-hand side, you have x minus a, squared, and then, let's see, these Sreeja Muraleedharan has taught 9th and 10th grade Algebra for over 6 years and graduate level Electronics for over 15 years. What I want to do in this video, it's gonna get a little Download Parabola Calculator App for Your Mobile, So you can calculate your values in your hand. Added Nov 21, 2015 by Team1 in Mathematics. It only takes a few minutes to setup and you can cancel any time. Looking for someone to help with your homework? Gamal Abdel Nasser Biography, Facts & Books | Who was Greek Creation Myth: Summary & Gods | The Creation in 1906 San Francisco Earthquake | Overview, Facts & Impact. From the source of Wikipedia: Cartesian coordinate system, Similarity to the unit parabola, Position of the focus. That's going to be 2y-- Do it in green, actually, Take any parabola equation, and find a, b, c values from equation. y minus b, times y minus b. It has absolutely helped me a lot! WebWrite the equation of the parabola Given the directrix y = 2 and focus (0, 8) find: The vertex. you're left with just a y, and then it's going to be y equals, y is equal to one over, two times, b minus k, and notice, b minus k is the difference between the y-coordinate of the focus, and the y-coordinate, Well, the Quadratic Formula Calculator helps to solve a given quadratic equation by using the quadratic equation formula. How can we calculate k then? Marisa Bjorland has taught math at the community college level since 2008, including remote and online courses. Given: A parabolas equation is y2 = 24x. Direct link to Nikhil Naidu's post It's not (b-k)^2 its b^2 , Posted 6 years ago. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Plus, get practice tests, quizzes, and personalized coaching to help you Determining mathematical problems can be difficult, but with practice it can become easier. What is the main difference of parabolas from hyperbolas? Can you determine the mathematic question in this equation? a y on the left-hand side, so let's divide everything So let's do that. Become a member to unlock the rest of this instructional resource and thousands like it. bit of a drum roll, we are just left with 1/2 times, b plus k. So, there you go. WebThis calculator will find either the equation of the hyperbola from the given parameters or the center, foci, vertices, co-vertices, (semi)major axis length, (semi)minor axis length, latera recta, length of the latera recta (focal width), focal parameter, eccentricity, linear eccentricity (focal distance), directrices, asymptotes, x-intercepts, You do not have a problem to solve as you have not written an equation. $$\begin{align*} {(x-h)}^2 & =4p(y-k)\\ {(x-4)}^2 & =-8(y-(-1))\\ \end{align*} $$. the same as that distance. focus of the x coordinate is \( \frac {-b}{(2a)} \), and y coordinate is \( c-\frac{b^2-1} { (4a)} \), Focus is \( (x,y) \) and Directrix equation \( y = c-\frac{b^2+1} { (4a)}\). WebFind equation of parabola given focus and directrix calculator. The focus of a parabola can be calculated by knowing the axis of the parabola, and the vertex of the parabola. What if the equation of a directrix isn't as simple as y=k or y= -k? {eq}\begin{align*} x & = 5-3\\ x & = 2\\ \end{align*} {/eq}. is, I just want to end up with just a y on the left-hand side, and just x's, ab's, and Geographic Interactions in Culture & the Environment, Geographic Diversity in Landscapes & Societies, Tools & Methodologies of Geographic Study, Physical Science - Water Balance: Homework Help, NY Regents - The American Revolution: Tutoring Solution, Reading Informational Texts: Tutoring Solution, Imperialism in the 19th and 20th Centuries: Help and Review, CSET Math: Geometric Description & Polar Coordinates. Step 1: Use the directrix to determine the orientation of the parabola. Well, we just apply the distance formula, or really, just the Pythagorean Theorem. The steps are easy and fun to follow along and teaches you a lot! Legendary app, i really like how the app allows you to grab problems with the camera, edit them, or just type them in long hand. It really works for me. It doesn't look like it, Example: If the focus of a parabola is (2,5) and the. The focus lies on the axis of symmetry of the parabola. This parabola is of the form {eq}{(y-k)}^2=4p(x-h) {/eq} so it opens horizontally. squared minus k squared, so these two are gonna be In the equations y=a(x-h)^2+k and x=a(y-k)^2+h where a=1/4p , (h,k ) represents vertex and p is the distance between focus and vertex . The vertex is halfway between the directrix and focus. Y coordinate. For those who struggle with math, equations can seem like an impossible task. The reason is because the squared terms are. So, the answer will be y 2 = 28 ( x + 3), which is not y 2 = 28 ( x + 1). From the paths of thrown baseballs, to fountains, even functions, to satellite, and radio waves. which would be equivalent to taking the absolute value of y minus k. So that's this distance right over here, and by the definition of a parabola, in order for (x,y) to be WebAn equation of a parabola is given. WebSteps to Find the Focus & Directrix of a Parabola Step 1: Identify the given equation and determine orientation of the parabola. All other trademarks and copyrights are the property of their respective owners. Question 1: Find vertex, focus, y-intercept, x-intercept, directrix, and axis of symmetry for the parabola equation y = 5x2+ 4x + 10? The signed distance from the directrix to the vertex is ${4\cdot3+3\cdot1-5\over5}=2$ and from the equation of the directrix the corresponding unit normal is $\frac15(4,3)$, so the focus is at Example: If the focus of a parabola is (2,5) and the Tap to unmute. on a's, b's, and k's, so let's do that. Even the parabola calculator helps to turn the equation into the vertex form through which you can readily find the crucial points of the parabola. WebWolfram|Alpha Widget: Parabola Calculator Parabola Calculator Enter the equation of parabola: Submit Computing Get this widget Build your own widget Browse widget to look like the parabolas that you remember from it looks really hairy, but it IS the equation of a parabola, and to show you that, we For further assistance, please Contact Us. WebFind the Parabola with Focus (1,2) and Directrix y=-2 (1,2) y=-2 | Mathway Algebra Examples Popular Problems Algebra Find the Parabola with Focus (1,2) and Directrix The following two examples will show how to find the focus and directrix of a parabola using the steps, definitions, and equations above. Find the surface area of the composite solid. So, for example, if I had a focus at the point, I don't know, let's say the point (1,2), and I had a directrix at y is equal to, I don't know, let's make it y is equal to -1, what would the equation Great app if you use it to learn, if you just use it to cheat shame on you. - [Voiceover] What I have This is very helpful. squared from both sides, so I can do that. Parabola calculator used to get quick results and obtain the graph for any given parabolic equation. Math is the study of numbers, space, and structure. Direct link to Bryan Ray's post Rotating a graph like thi, Posted 8 years ago. b squared minus k squared, plus b squared minus k squared. Well let's get the k squared on this side, so let's subtract k WebFocus and directrix of a parabola Equation of a parabola from focus & directrix CCSS.Math: HSG.GPE.A.2 Google Classroom You might need: Calculator Write the gives me the correct solution in seconds with the easiest calculation. Semele Genealogy & Mythology | Who is Semele in Greek Delhi Sultanate History & Rulers | What was the Delhi Maya Religion Overview, Gods & Rituals | The Religion of Wadjet Symbol, Facts & Overview | Snake Egyptian Goddess. The focus of a parabola can be calculated by knowing the axis of the parabola, and the vertex of the parabola. She has a master's degree in mathematics from University of California, Santa Cruz and a bachelor's degree in mathematics from University of California, San Diego. Parabola is a curve where any point is at an equal distance from a fixed point (focus) and a fixed straight line (directrix). Determine mathematic question. have a parabola where the y-coordinate of the focus is lower than the y-coordinate simplify this on your own, it's just gonna be a little Parabola Calculator with focus and directrix. where would you learn how to graph a parabola with a diagonal directrix? Math can be a difficult subject for many people, but there are ways to make it easier. Translating a parabola vertically gives you an opportunity to produce a new parabola. Can someone explain to me why the square root doesnt cancel out the squared terms? for this to be a parabola, it has to be equidistant to However, a parabola equation finder will support calculations where you need to apply the standard form. How to Derive the Equation of a Parabola Given its Focus & Directrix. If we rotate the parabola, then its vertex is: \( (h,k) \). We always struggled to serve you with the best online calculations, thus, there's a humble request to either disable the AD blocker or go with premium plans to use the AD-Free version for calculators. If you know the coordinates of the focus and the equation of the directrix, you can use this information to deduce the equation of the parabola.You can follow the steps below, or use the calculator on the left to find the parabola's equation. WebMore. Find the coordinates of the focus and the equation of the directrix for the parabola given by the equation {eq}{(x-4)}^2=-8(y+1) {/eq}. lessons in math, English, science, history, and more. If a>0, parabola is upward, a0, parabola is downward. where {eq}(h, k) {/eq} is the vertex of the parabola and {eq}p {/eq} is the distance between the vertex and the focus/directrix. A hyperbola results from the intersection of the plane and the cone, but with the plane at a position that is not parallel to the side of the cone. Find Equation of Parabola given Focus and Directrix 7.2. us a positive value, and you need a non-negative value if you're talking about distances, but you can definitely WebFocus of Parabolic Reflector Calculator Formula for the Focal Distance of a Parabolic Reflector Given its Depth and Diameter The equation of a parabola with vertical axis and vertex at the origin is given by y = 1 4 f x 2 where f is the focal distance which is the distance between the vertex V and the focus F . $$\begin{align*} {(y-k)}^2 & =4p(x-h)\\ {(y-2)}^2 & =12(x-5)\\ \end{align*} $$. This symmetrical plane curve made by the intersection of a right circular cone with a plane surface. Step 1: Identify the given equation and determine orientation of the parabola. Parabola can be seen in nature or in man made items. document.write("- "+yr); Good Calculators: Significant Figures Calculator. It also gives you explanations if you pay for the premium version. Everybody needs a calculator at some point, get the ease of calculating anything from the source of calculator-online.net. Can I use the general equation to compare and solve the problem? The point is called parabola focus and the line is known as directrix of parabola. Webto find equation of the directrix, y = p use p to find the endpoints of the latus rectum, ( 2p, p) Plot the focus, directrix, and latus rectum, and draw a smooth curve to form the parabola. Direct link to Vu's post That is true for the left. Direct link to Jesse's post In this case, the formula, Posted 8 years ago. Math is all about solving equations and finding the right answer. bit of hairy algebra, so hopefully you see that I'm your childhood, (chuckles) if you do remember parabolas WebEquation of a parabola given focus and directrix calculator Take any parabola equation, and find a, b, c values from equation substitute those values in Vertex v(h, k). Let's say we take this its focus and its directrix, so what does that mean? Unlock Skills Practice and Learning Content. The equation of a parabola is derived from the focus and directrix, and then the general formula is used to solve an example. A parabola is set of all points in a plane which are equal distance from a given point and given line. Example 1: Graphing a Parabola with Vertex (0, 0) and the x -axis as the Axis of Symmetry Graph y2 = 24x. So what we really want is on the left-hand side, you're gonna get y minus k, squared is equal to x minus a, squared, plus y minus b, squared. Now what I want to do (chuckles) That's going to be 2yb minus 2yk. Well, it would be y is equal to one over, two times, b minus k, so two minus -1, that's the same thing as two plus one, so that's just three, two minus -1 is three, times x minus one, squared, plus 1/2 times, b plus k. Two plus -1 is one, so one, and so what is this going to be? 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