# How do you graph y = 3x^2 + 8x - 6?

Aug 2, 2015

Graph $y = 3 {x}^{2} + 8 x - 6$

#### Explanation:

To graph a parabola, find first a few critical points. They are: vertex, axis of symmetry, y intercept, and x-intercepts.
a> 0 --> the parabola opens upward.
x- coordinate of vertex and axis of symmetry: $x = - \frac{b}{2 a} = - \frac{8}{6} = - \frac{4}{3}$
y-coordinate of vertex:$y = f \left(- \frac{4}{3}\right)$=
y intercept --> x = 0 --> y = -6
x-intercepts: solve y = 0
$D = {d}^{2} = {b}^{2} - 4 a c = 64 + 72 = 136$ --> $d = \pm 2 \sqrt{34}$
$x = \pm - \frac{8}{6} \pm \frac{2 \sqrt{34}}{6} = - \frac{8}{3} \pm \frac{\sqrt{34}}{3}$
graph{3x^2 + 8x - 6 [-40, 40, -20, 20]}