Answer:
see attachment
Step-by-step explanation:
The given equation is
[tex] - \frac{1}{2} {x}^{2} + 2 = 2 {x}^{2} - 8[/tex]
The graph of the left hand side of this equation is
[tex]y = - \frac{1}{2}{x}^{2} + 2[/tex]
This quadratic graph has its vertex at (0,2) and turns upside down.
The right hand side of the equation is
[tex]y = 2 {x}^{2} - 8[/tex]
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).
