Answer:
y = 3x² + 54x + 240
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (- 9, - 3), thus
y = a(x + 9)² - 3
To find a substitute either of the roots into the equation
Using (- 8, 0), then
0 = a(- 8 + 9)² - 3
0 = a - 3 ( add 3 to both sides )
a = 3
y = 3(x + 9)² - 3 ← in vertex form
Expand factor and simplify
y = 3(x² + 18x + 81) - 3
= 3x² + 54x + 243 - 3
= 3x² + 54x + 240 ← in standard form
