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

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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.

Algebra 2

## 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 $(-2,0$), $(2,0)$, and $(3,-15)$. Write your answer in the form $y = a(x - p)(x - q)$, where $a$, $p$, and $q$ are integers, decimals, or simplified fractions.
Solution:
1. Identify $p$ and $q$: Identify the values of $p$ and $q$ from the given $x$-intercepts of the parabola.$\newline$Since the parabola passes through $(-2,0)$ and $(2,0)$, these points are the $x$-intercepts of the parabola. Therefore, $p = -2$ and $q = 2$.
2. Write general form: Write the general form of the parabola using the identified values of $p$ and $q$. $\newline$The general form of the parabola is $y = a(x - p)(x - q)$. $\newline$Substituting $p = -2$ and $q = 2$, we get $y = a(x + 2)(x - 2)$.
3. Find value of $a$: Use the third point $(3, -15)$ to find the value of $a$. $\newline$Substitute $x = 3$ and $y = -15$ into the equation $y = a(x + 2)(x - 2)$ to solve for $a$.$\newline$ $-15 = a(3 + 2)(3 - 2)$ $-15 = a(5)(1)$ $\newline$$-15 = 5a$$a=-3$
4. Write final equation: Write the final equation of the parabola using the found value of $a$.$\newline$Substitute $a = -3$ into the equation $y = a(x + 2)(x - 2)$ to get the final equation of the parabola. $\newline$$y = -3(x + 2)(x - 2)$

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