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

Identify p and q: Identify the values of p and q from the given points where the parabola crosses the x-axis. The points (-3, 0) and (2, 0) are where the parabola intersects the x-axis, so these are our p and q values. Therefore, p = -3 and q = 2.Write general form: Write the general form of the parabola using the values of p and q. The general form of the parabola is y = a(x - p)(x - q). Substituting p = -3 and q = 2, we get y = a(x + 3)(x - 2).Solve for value of a: Use the remaining point (-1, 12) to solve for the value of a. Substitute x = -1 and y = 12 into the equation y = a(x + 3)(x - 2). 12 = a(-1 + 3)(-1 - 2) 12 = a(2)(-3) 12 = -6a a = -2Write final equation: Write the final equation of the parabola using the value of a. Substitute a = -2 into the equation y = a(x + 3)(x - 2). y = -2(x + 3)(x - 2)

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Write the equation of the parabola that passes through the points $(-3,0$ ), $(-1,12$ ), and $(2,0$ ). $\newline$ 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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Math Problems

Algebra 1

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

(-1,12

), and

(2,0

\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 $p$ and $q$ : Identify the values of $p$ and $q$ from the given points where the parabola crosses the x-axis. $\newline$ The points $(-3, 0)$ and $(2, 0)$ are where the parabola intersects the x-axis, so these are our $p$ and $q$ values. $\newline$ Therefore, $p = -3$ and $q = 2$ .
Write general form: Write the general form of the parabola using the values of $p$ and $q$ . The general form of the parabola is $y = a(x - p)(x - q)$ . Substituting $p = -3$ and $q = 2$ , we get $y = a(x + 3)(x - 2)$ .
Solve for value of $a$ : Use the remaining point $(-1, 12)$ to solve for the value of $a$ . Substitute $x = -1$ and $y = 12$ into the equation $y = a(x + 3)(x - 2)$ . $12 = a(-1 + 3)(-1 - 2)$ $12 = a(2)(-3)$ $12 = -6a$ $a = -2$
Write final equation: Write the final equation of the parabola using the value of $a$ . $\newline$ Substitute $a = -2$ into the equation $y = a(x + 3)(x - 2)$ . $\newline$ $y = -2(x + 3)(x - 2)$