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

Jun 3, 2015

y = 2x^2 + 12x - 7

x of vertex: $x = \left(- \frac{b}{2} a\right) = - \frac{12}{4} = - 3$

y of vertex:$f \left(- 3\right) = 18 + 36 - 7 = 47$

Vertex form: $f \left(x\right) = 2 \left({x}^{2} + 3\right) + 47$

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

x- intercepts: $y = 2 {x}^{2} + 12 x - 7 = 0.$

$D = {d}^{2} = 144 + 56 = 200$--> $d = \pm 20$

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