Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=-(2x+6)^{2}+3[/tex]
Factor the leading coefficient
[tex]y=-(2(x+3))^{2}+3[/tex]
[tex]y=-4(x+3)^{2}+3[/tex]
This is the equation of a vertical parabola in vertex form
The parabola open downward
The vertex is a maximum
The vertex is the point (-3,3)
Find out the x-intercepts (values of x when the value of y is equal to zero)
For y=0
[tex]0=-4(x+3)^{2}+3[/tex]
[tex]4(x+3)^{2}=3[/tex]
[tex](x+3)^{2}=(3/4)[/tex]
square root both sides
[tex](x+3)=(+/-)\frac{\sqrt{3}}{2}[/tex]
[tex]x=-3(+/-)\frac{\sqrt{3}}{2}[/tex]
[tex]x1=-3+\frac{\sqrt{3}}{2}[/tex] ----->[tex]x1=-2.134[/tex]
[tex]x2=-3-\frac{\sqrt{3}}{2}[/tex] ----->[tex]x2=-3.866[/tex]
using a graphing tool
The graph in the attached figure
