Question

Graph ​ g(x)=−2x2−12x−24 ​.

Answer 1

Answer:

See graph in attachment

Step-by-step 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 $a=-2\:$

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 $-3$ 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.