Question

the solutions to the inequality y > −3x 2 are shaded on the graph. which point is a solution? a). (0, 2) b). (2, 0) c). (1, −2) d). (−2, 1)

Answer 1

(2,0)

All the other points listed are in the side of points that do not belong to the set of soluctions.

Answer 2

we have

`y> -3x+2`

The solution is the shaded area above the dotted line

we know that

If a point is a solution of the inequality, then the coordinates of the point must satisfy the inequality

We will verify all cases to determine the solution of the problem

Case A) Point
`(0,2)`

`x=0\\y=2`

Substitute the value of x and y in the inequality and verify

`2> -3*0+2`

`2>2` -------> is not true

therefore

the point
`(0,2)` is not a solution of the inequality

Case B) Point
`(2,0)`

`x=2\\y=0`

Substitute the value of x and y in the inequality and verify

`0> -3*2+2`

`0>-4` -------> is true

therefore

the point
`(2,0)` is a solution of the inequality

Case C) Point
`(1,-2)`

`x=1\\y=-2`

Substitute the value of x and y in the inequality and verify

`-2> -3*1+2`

`-2>-1` -------> is not true

therefore

the point
`(1,-2)` is not a solution of the inequality

Case D) Point
`(-2,1)`

`x=-2\\y=1`

Substitute the value of x and y in the inequality and verify

`1> -3*(-2)+2`

`1>8` -------> is not true

therefore

the point
`(-2,1)` is not a solution of the inequality

therefore

the answer is the Point B

`(2,0)`

To better understand the problem see the attached figure