Question

How do you graph `y > 2x^2 − 3` and `y < -x^2+8`?

Answer 1

Graph and solve the system
y > 2x^2 - 3 (1)
y < -x^2 + 8 (2)

Explanation:

First, graph the parabola y1 = 2x^2 - 3.
The solution set of inequality (1) is the area above the parabola y1. Color or shade it.
Next, graph the parabola y2 = - x^2 + 8.
The solution set of inequality (2) is the area below the parabola y2.
The compound solution set is the commonly shared area.
graph{2x^2 - 3 [-10, 10, -5, 5]}
graph{- x^2 + 8 [-20, 20, -10, 10]}