Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1). me

A(x - (-9))(x - (-3)) = a(x - (-6))² + (-1)

a(x + 9)(x + 3) = a(x + 6)² - 1

a(x² + 3x + 9x + 27) = a(x² + 12x + 36) - 1

ax² + 12ax + 27a = ax² + 12ax + 36a - 1

27a = 36a - 1    |subtract 36a from both sides

-9a = -1    |divide both sides by (-9)

a = 1/9

ax² = 1/9x²

12ax = 12·1/9x = 4/3x

27a = 27·1/9 = 3

y = 1/9x^2 + 4/3x + 3