Respuesta :
Answer:
see explanation
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) = (- 6, - 1), thus
y = a(x + 6)² - 1
To find a substitute one of the roots into the equation
Using (- 3, 0), then
0 = a(- 3 +6)² - 1
0 = 9a - 1 ( add 1 to both sides )
1 = 9a ( divide both sides by 9 )
a = [tex]\frac{1}{9}[/tex], thus
y = [tex]\frac{1}{9}[/tex](x + 6)² - 1 ← in vertex form
Expand factor and simplify
y = [tex]\frac{1}{9}[/tex] (x² + 12x + 36) - 1 ← distribute
y = [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 4 - 1
= [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 3 ← in standard form
