Answer to Question #254561 in Algebra for Charm

Question

find the coordinates of points that belong to the solution set of inequality y <3x ²+3x-6 a.(-1,2) b.(1,-7) c.(-2,7) d.(-1,-1)

Answer 1

$y\lt3x^2+3x-6$

For a.(-1,2)

2$\lt 3(-1)^2+3(-1)-6$

$2\lt$ -6

The inequality is not satisfied.

b.(1,-7)

-7$\lt3\times 1^2+3(1)-6$

-7<0

The coordinates belongs to the inequality

for (-2,7)

$y\lt3(-2)^2+3(-2)-6$

$7\lt3(-2)^2+3(-2)-6$

for (-1, -1)

-1$\lt 3(-1)^2+3(-1)-6$

$-1\lt -6$ (not satisfied)

So, only point (1,-7) belongs to the solution set of the inequality.