# How do you identify the important parts of y = –2x^2 – 32x – 126 to graph it?

Sep 30, 2015

Graph $y = - 2 {x}^{2} - 32 x - 126$

#### Explanation:

The important parts to find are:
x-coodinate of vertex and axis of symmetry:
$x = \left(- \frac{b}{2} a\right) = \frac{32}{4} = 8$
y-coordinate of vertex:
y = f(8) = -2(64) - 32(-8) - 126 = 2
y-intercept --> Make x = 0 --> y = -126
x-intercepts --> Make x = 0, solve y = 0
$y = - 2 \left({x}^{2} + 16 x + 63\right) = 0.$
Roots have same sign, Factor pairs of (63) --> (3, 31)(7, 9). This sum is 16 = b. Then the 2 x-intercepts (real roots) are : 7 and 9
graph{-2x^2 - 32x - 126 [-10, 10, -5, 5]}