Find the vertex form of a parabola with a vertex of (-2, 12)

that passes through (-4, 0)

y = - 3 (x + 2) ² + 12

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) = ( - 2, 12), thus

y = a (x + 2) ² + 12

To find a substitute ( - 4, 0) into the equation

0 = a ( - 2) ² + 12, that is

4a + 12 = 0 (subtract 12 from both sides)

4a = - 12 (divide both sides by 4)

a = - 3

y = - 3 (x + 2) ² + 12 ← equation in vertex form