Question

Which of the following graphs is described by the function given below? y = 2x 2 + 6x + 3

Answer 1

Answer: graph a

Step-by-step explanation: a p e x

Answer 2

The graph in the attached figure

Explanation:

we have

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

This is the equation of a vertical parabola open up

The vertex is a minimum

Convert to vertex form

Complete squares

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

Factor the leading coefficient

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

`y-3+4.5=2(x^(2)+3x+2.25)`

`y+1.5=2(x^(2)+3x+2.25)`

Rewrite as perfect squares

`y+1.5=2(x+1.5)^(2)`

The vertex is the point (-1.5,-1.5)

Find the zeros of the function

For y=0

`2(x+1.5)^(2)=1.5`

`(x+1.5)^(2)=3/4`

square root both sides

`x+(3)/(2) =(+/-)(√(3))/(2)`

`x=-(3)/(2)(+/-)(√(3))/(2)`

`x=-(3)/(2)(+)(√(3))/(2)=(-3+√(3))/(2)=-0.634`

`x=-(3)/(2)(-)(√(3))/(2)=(-3-√(3))/(2)=-2.366`

Find the y-intercept

For x=0

`y=3`

The y-intercept is the point (0,3)

therefore

The graph in the attached figure