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

11.82 kmStep-by-step explanation:Hi! All u have to do is 6.37 km x 5.45 km which is (look at answer part)Hope this helped :DUwU...

Which of the following graphs is described by the

rue61

13.03.2022

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

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