# How do you identify the important parts of y= 6x^2 +2x+4 to graph it?

Oct 3, 2015

Graph $y = 6 {x}^{2} + 2 x + 4$

#### Explanation:

The important parts to graph y are:
a. x-coordinate of vertex and axis of symmetry:
$x = \left(- \frac{b}{2} a\right) = - \frac{2}{12} = - \frac{1}{6}$
y-coordinate of vertex:
$y = f \left(- \frac{1}{6}\right) = \frac{1}{6} - \frac{2}{6} + 4 = \frac{23}{6.}$
b. y-intercept. Make x = 0 --> y = 4
x-intercepts. Make y = 0 and solve $6 {x}^{2} + 2 x + 4 = 0.$
Since D = 4 - 96 < 0, there are no x-intercepts (no real roots). The parabola is completely above the x-axis and it opens upward (a > 0).
graph{6x^2 + 2x + 4 [-40, 40, -20, 20]}