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Write the equation of the parabola that passes through the points $(-3,0$ ), $(-2,-12$ ), and $(1,0$ ). $\newline$ Write your answer in the form $y = a(x - p)(x - q)$ , where $a$ , $p$ , and $q$ are integers, decimals, or simplified fractions.

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. Write the equation of the parabola that passes through the points

(-3,0

),

(-2,-12

), and

(1,0

).

\newline

Write your answer in the form

y = a(x - p)(x - q)

, where

a

,

p

, and

q

are integers, decimals, or simplified fractions.

Identify x-intercepts: Identify the x-intercepts from the given points. $\newline$ The x-intercepts are the x-values of the points where the y-values are zero. $\newline$ x-intercepts: $-3$ , $1$
Write equation in form: Use the $x$ -intercepts to write the equation in the form $y = a(x - p)(x - q)$ .
$p = -3$
$q = 1$
$y = a(x - p)(x - q)$
$y = a(x + 3)(x - 1)$
Find value of 'a': Use the point $(-2,-12)$ to find the value of 'a'. $\newline$ $y = a(x + 3)(x - 1)$ $\newline$ $-12 = a(-2 + 3)(-2 - 1)$ $\newline$ $-12 = a(1)(-3)$ $\newline$ $-12 = -3a$ $\newline$ $a = 4$
Final equation of parabola: Write the final equation of the parabola using the value of $a$ and the x-intercepts. $a = 4$ $p = -3$ $q = 1$ $y = a(x - p)(x - q)$ $y = 4(x + 3)(x - 1)$

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