Question

Which graph correctly solves the equation below?

three fourths x squared minus three equals negative three fourths x squared plus three

Two quadratic graphs opening up. They intersect at 0 and negative 3.
One quadratic graph opening up and one quadratic graph facing down. They intersect at 0, 3.
Quadratic graph opening up and quadratic graph opening down. They intersect at 0, negative 3.
Two parabolas one facing down with a vertex at 0, 3 and one facing up with a vertex at 0, negative 3

Answer 1

D

Explanation:

^^

Answer 2

Two parabolas one facing down with a vertex at 0, 3 and one facing up with a vertex at 0, negative 3

Explanation:

we have

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

This equation is equivalent to solve for x the following system of equations

`y=(3)/(4)x^(2)-3` ----> equation A

This is the equation of a vertical parabola open up with vertex at (0,-3)

`y=-(3)/(4)x^(2)+3` ----> equation B

This is the equation of a vertical parabola open down with vertex at (0,3)

Solve the system of equations by graphing

The solutions are the x-coordinates of the intersection point both graphs

using a graphing tool

The solution is x=-2, x=2

see the attached figure