Question

Which of the following coordinates of points belong to the solution set of the inequality y <2x² +3x - 5?

A.(-3,2)
B.(-2,9)
C.(1,6)
D.(3,1)
E. (-1.5)​

Answer 1

A , D

Explanation:

Check the inequality for each point.

For A. (-3,2)

`y < {2x}^(2) + 3x - 5 \\ 2 < {2 ( - 3)}^(2) + 3( - 3) - 5 \\ 2 < 2 * 9 - 9 - 5 \\ 2 < 18 - 9 - 5 \\ 2 < 4 \\`

The inequality is satisfied.

For B. (-2,9)

`y < {2x}^(2) + 3x - 5 \\ 9 < 2 {( - 2)}^(2) + 3( - 2) - 5 \\ 9 < 2(4) - 6 - 5 \\ 9 < 8 - 6 - 5 \\ 9 < - 3 \\`

The inequality is not satisfied.

For C. (1,6)

`y < {2x}^(2) + 3x - 5 \\ 6 < {2(1)}^(2) + 3(1) - 5 \\ 6 < 2(1) + 3 - 5 \\ 6 < 2 + 3 - 5 \\ 6 < 0`

The inequality is not satisfied.

For D. (3,1)

`y < {2x}^(2) + 3x - 5 \\ 1 < {2(3)}^(2) + 3(3) - 5 \\ 1 < 2(9) + 9 - 5 \\ 1 < 18 + 9 - 5 \\ 1 < 22 \\`

The inequality is satisfied.

For E. (-1,5)

`y < {2x}^(2) + 3x - 5 \\ 5 < {2( - 1)}^(2) + 3( - 1) - 5 \\ 5 < 2(1) - 3 - 5 \\ 5 < 2 - 3 - 5 \\ 5 < - 6 \\`

The inequality is not satisfied.