write the equation of the parabola shown in the graph. write your answer in standard form, y = ax² + bx + c…

Explanation:

Step1: Use factored - form of parabola

Since the parabola has x - intercepts at $x=-5$ and $x = - 4$, the factored form of the parabola is $y=a(x + 5)(x + 4)$.

Step2: Find the value of a

Substitute the point $(-6,-8)$ into the equation $y=a(x + 5)(x + 4)$. We get $-8=a(-6 + 5)(-6 + 4)$. Simplify the right - hand side: $-8=a(-1)(-2)$, so $-8 = 2a$. Solve for a: $a=-4$.

Step3: Expand the factored form

$y=-4(x + 5)(x + 4)=-4(x^{2}+4x+5x + 20)=-4(x^{2}+9x + 20)=-4x^{2}-36x - 80$.

Answer:

$y=-4x^{2}-36x - 80$