Question

ILL MARK BRAINLIEST ASAP IF CORRECT Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1).

Answer 1

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 = $\frac{1}{9}$, thus

y = $\frac{1}{9}$(x + 6)² - 1 ← in vertex form

Expand factor and simplify

y = $\frac{1}{9}$ (x² + 12x + 36) - 1 ← distribute

y = $\frac{1}{9}$ x² + $\frac{4}{3}$ x + 4 - 1

  = $\frac{1}{9}$ x² + $\frac{4}{3}$ x + 3 ← in standard form