Question

Which graph is the graph of the following inequality? y ≤ 1/2 (x-6)^2 + 2

Answer 1

ANSWER

The graph in option D

EXPLANATION

The given inequality is

$y \leqslant \frac{1}{2} {(x - 6)}^{2} + 2$

To graph this inequality, we must first of all

graph the corresponding quadratic function.

$y = \frac{1}{2} {(x - 6)}^{2} + 2$

This is a minimum graph with vertex

$(6,2)$

We graph this equation with a solid line.

We then test the inequality using (0,0),

$0 \leqslant \frac{1}{2} {(0- 6)}^{2} + 2$

$0 \leqslant 20$

This statement is true so we shade the lower half plane to obtain the graph in option D.