Graph g(x)=−2x2−12x−24 .

Question

asked Jun 12, 2020 189k views

2 Answers

Warren Chu · Answer 1 · 2020-06-17T01:50:24+0000

Answer:

See graph in attachment

Explanation:

We want to graph the function,

g(x)=-2x^2-12x-24

First, let us rewrite the function in the vertex form;

g(x)=-2(x^2+6x)-24

$\Rightarrow g(x)=-2(x^2+6x+(3)^2)--2(-3)^2-24$

$\Rightarrow g(x)=-2(x^2+6x+(3)^2)+2(9)-24$

$\Rightarrow g(x)=-2(x+3)^2+18-24$

$\Rightarrow g(x)=-2(x+3)^2-6$

The parabola opens downwards because
$a=-2\:<\:0$

The vertex of the parabola is
(-3,-6) .

At y-intercept,
x=0 .

This implies that,

g(0)=-2(0+3)^2-6=-18-6=-24

At x-intercept,
y=0

This implies that;

$\Rightarrow 0=-2(x+3)^2-6$

$\Rightarrow -2(x+3)^2=6$

$\Rightarrow (x+3)^2=-3$

This equation has no real number solutions because of
on the right hand side. This implies that the graph has no x-intercepts.

We therefore draw a maximum graph through the vertex and the y-intercept to obtain the graph in the attachment.