Answer:
D
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) = (- 3, - 6), thus
y = a(x + 3)² - 6
To find a substitute (0, 0) into the equation
0 = 9a - 6 ⇒ a = [tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex]
y = [tex]\frac{2}{3}[/tex](x + 3)² - 6 ← in vertex form
Expand (x + 3)² and distribute by [tex]\frac{2}{3}[/tex]
y = [tex]\frac{2}{3}[/tex](x² + 6x + 9) - 6
= [tex]\frac{2}{3}[/tex] x² + 4x + 6 - 6
= [tex]\frac{2}{3}[/tex] x² + 4x ← in standard form
