Question

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

Answer 1

Answer:

The graph in the attached figure

Step-by-step 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

$x+\frac{3}{2} =(+/-)\frac{\sqrt{3}}{2}$

$x=-\frac{3}{2}(+/-)\frac{\sqrt{3}}{2}$

$x=-\frac{3}{2}(+)\frac{\sqrt{3}}{2}=\frac{-3+\sqrt{3}}{2}=-0.634$

$x=-\frac{3}{2}(-)\frac{\sqrt{3}}{2}=\frac{-3-\sqrt{3}}{2}=-2.366$

Find the y-intercept

For x=0

$y=3$

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

therefore

The graph in the attached figure