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Write Quadratic Function Given `X`-Intercepts And Another Point

Write Quadratic Function Given `X`-Intercepts And Another Point Worksheet

Algebra 2
Quadratic Functions

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How Will This Worksheet on 'Write Quadratic Function Given `x`-Intercepts and Another Point' Benefit Your Student's Learning?

  • Aids in understanding the creation and graphical behavior of quadratic functions.
  • Enhances comprehension of intercepts and demonstrates how a point determines the coefficient.
  • Fosters critical thinking by requiring students to identify `x`-intercepts from given points.
  • Strengthens algebraic skills by applying theoretical knowledge to practical problems.
  • Prepares students for advanced mathematical concepts and real-world applications.

How to Write Quadratic Function Given `x`-Intercepts and Another Point?

  • Determine the values of \(p\) and \(q\).
  • Substitute \(p\), \(q\), and the \(x\) and \(y\) values from the third point into the equation.
  • Simplify the equation to find the value of \(a\).
  • Write the quadratic function in the form \( f(x) = a(x - p)(x - q) \) by substituting the value of \(a\).

Solved Example

Q. Write the equation of the parabola that passes through the points (−2,0(-2,0), (2,0)(2,0), and (3,−15)(3,-15). Write your answer in the form y=a(x−p)(x−q)y = a(x - p)(x - q), where aa, pp, and qq are integers, decimals, or simplified fractions.
Solution:
  1. Identify pp and qq: Identify the values of pp and qq from the given xx-intercepts of the parabola.\newlineSince the parabola passes through (−2,0)(-2,0) and (2,0)(2,0), these points are the xx-intercepts of the parabola. Therefore, p=−2p = -2 and q=2q = 2.
  2. Write general form: Write the general form of the parabola using the identified values of pp and qq. \newlineThe general form of the parabola is y=a(x−p)(x−q)y = a(x - p)(x - q). \newlineSubstituting p=−2p = -2 and q=2q = 2, we get y=a(x+2)(x−2)y = a(x + 2)(x - 2).
  3. Find value of aa: Use the third point (3,−15)(3, -15) to find the value of aa. \newlineSubstitute x=3x = 3 and y=−15y = -15 into the equation y=a(x+2)(x−2)y = a(x + 2)(x - 2) to solve for aa.\newline −15=a(3+2)(3−2)-15 = a(3 + 2)(3 - 2) −15=a(5)(1)-15 = a(5)(1) \newline−15=5a-15 = 5aa=−3a=-3
  4. Write final equation: Write the final equation of the parabola using the found value of aa.\newlineSubstitute a=−3a = -3 into the equation y=a(x+2)(x−2)y = a(x + 2)(x - 2) to get the final equation of the parabola. \newliney=−3(x+2)(x−2)y = -3(x + 2)(x - 2)
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About Worksheet

Algebra 2
Quadratic Functions

Writing a quadratic function from its `x`-intercepts and an additional point involves finding the equation using two `x`-intercepts and a third point. First, identify the `x`-intercepts from the two points where the `y`-coordinate is `0`. Then, use the third point to determine the coefficient \(a\) in the quadratic function. The function is represented as \( f(x) = a(x - p)(x - q) \), where \(p\) and \(q\) are the `x`-intercepts.

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