Question

How do you write the quadratic in vertex form given `y=-3x^2-24x+7`?

Answer 1

Coordinates of vertex :

`x = -b/(2a) = 24/-6 = -4`

y = f(-b/2a) = f(-4) = -3(16) - 24(-4) + 7 = -48 + 96 + 7 = 55

Vertex form: `y = -3.(x + 4)^2 + 55`

Check:

`Develop: -3(x + 4)^2 + 55 = -3.(x^2 + 8x + 16) + 55` =
`= -3x^2 - 24x - 48 + 55 = -3x^2 - 24x + 7.` Correct