Question

How do you write `y = 2x^2 + 12x - 7` in vertex form and identify the vertex, y intercept and x intercept?

Answer 1

y = 2x^2 + 12x - 7

x of vertex: `x = (-b/2a) = -12/4 = -3`

y of vertex:`f(-3) = 18 + 36 - 7 = 47`

Vertex form: `f(x) = 2(x^2 + 3) + 47`

Y-intercept. Make x = 0 --> y = -7

x- intercepts: `y = 2x^2 + 12x - 7 = 0.`

`D = d^2 = 144 + 56 = 200`--> `d = +-20`

x = -3 +- 20/4 = -3 +- 5