Write the equation of the parabola that passes through the points (-5,0), (-7,-40), 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 Intercepts: We have the points (-5,0), (-7,-40), and (-2,0). The points (-5,0) and (-2,0) are the x-intercepts of the parabola, so they give us the values of p and q directly. p = -5 and q = -2.Write Parabola Equation: Now we can write the equation of the parabola in the form y = a(x - p)(x - q) using the values of p and q we found. y = a(x + 5)(x + 2)Find Value of a: Next, we need to find the value of a. We will use the point (-7,-40) to do this. Substitute x = -7 and y = -40 into the equation y = a(x + 5)(x + 2). -40 = a(-7 + 5)(-7 + 2)Simplify Equation: Simplify the equation to solve for a. -40 = a(-2)(-5) -40 = 10a a = -40 / 10 a = -4Final Equation: Now that we have found a = -4, we can write the final equation of the parabola. y = -4(x + 5)(x + 2)

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Write the equation of the parabola that passes through the points $(-5,0$ ), $(-7,-40$ ), 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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Algebra 1

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

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

(-5,0

(-7,-40

), 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 Intercepts: We have the points $(-5,0$ ), $(-7,-40$ ), and $(-2,0$ ). The points $(-5,0$ ) and $(-2,0$ ) are the $x$ -intercepts of the parabola, so they give us the values of $p$ and $q$ directly. $p = -5$ and $q = -2$ .
Write Parabola Equation: Now we can write the equation of the parabola in the form $y = a(x - p)(x - q)$ using the values of $p$ and $q$ we found. $\newline$ $y = a(x + 5)(x + 2)$
Find Value of a: Next, we need to find the value of $a$ . We will use the point $(-7,-40)$ to do this. Substitute $x = -7$ and $y = -40$ into the equation $y = a(x + 5)(x + 2)$ . $\newline$ $-40 = a(-7 + 5)(-7 + 2)$
Simplify Equation: Simplify the equation to solve for $a$ . $\newline$ $-40 = a(-2)(-5)$ $\newline$ $-40 = 10a$ $\newline$ $a = -40 / 10$ $\newline$ $a = -4$
Final Equation: Now that we have found $a = -4$ , we can write the final equation of the parabola. $y = -4(x + 5)(x + 2)$