Question

How is the graph of the quadratic function to produce the graph of y=-(2x+6)^2+3

Answer 1

The graph in the attached figure

Explanation:

we have

`y=-(2x+6)^(2)+3`

Factor the leading coefficient

`y=-(2(x+3))^(2)+3`

`y=-4(x+3)^(2)+3`

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

`0=-4(x+3)^(2)+3`

`4(x+3)^(2)=3`

`(x+3)^(2)=(3/4)`

square root both sides

`(x+3)=(+/-)(√(3))/(2)`

`x=-3(+/-)(√(3))/(2)`

`x1=-3+(√(3))/(2)` ----->
`x1=-2.134`

`x2=-3-(√(3))/(2)` ----->
`x2=-3.866`

using a graphing tool

The graph in the attached figure