Question

Which Graph correctly solves the equation below? -1/2x^2 +2 = 2x^2 -8

Answer 1

Answer:

see attachment

Step-by-step explanation:

The given equation is

$- \frac{1}{2} {x}^{2} + 2 = 2 {x}^{2} - 8$

The graph of the left hand side of this equation is

$y = - \frac{1}{2}{x}^{2} + 2$

This quadratic graph has its vertex at (0,2) and turns upside down.

The right hand side of the equation is

$y = 2 {x}^{2} - 8$

This quadratic graph opens upwards and has its vertex at (0,-8).

The two graphs intersects at two points , which are (-2,0) and (2,0).