Question

Graph ​ g(x)=−2x2−12x−24 ​.

Answer 1

-3,-6 and -2,-8

Explanation:

took the test

Answer 2

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
`-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.