Create the equation of a quadratic function, in standard form

f(x) = 4x² + 8x - 12

Step-by-step explanation:

f(x) = ax² + bx + c , a ≠ 0

Coordinates of vertex are ( - 1, - 16)

x-coordinate of vertex is ( - )

- = - 1 ⇒ b = 2a

y-coordinate of vertex is ( )

= - 16

a(- 3)² + 2a(- 3) + c = 0 ⇒ c = - 3a

4a(- 3a) - (2a)² = - 64a

- 12a² - 4a² = - 64a ...... (1)

(1) ÷ (- 4a)

4a = 16 ⇒ a = 4

b = 8

c = - 12

f(x) = 4x² + 8x - 12