To determine whether a point is a solution of the inequality $y < 2x^2 + 3x - 5$, we will plug in the coordinates of each point $(x, y)$ into the inequality and check whether the inequality holds.

Given Inequality:

$y < 2x^2 + 3x - 5$

Example:

For point $(-1, 6)$: $y < 2x^2 + 3x - 5$ Substituting $(-1, 6)$ into the inequality: $6 < 2(-1)^2 + 3(-1) - 5$ $6 < 2(1) - 3 - 5$ $6 < 2 - 3 - 5$ $6 < -6 \quad \text{(False)}$ So, point $(-1, 6)$ is not a solution.

Now let's evaluate the other points:

2. Point $(1, 8)$:

Substitute $x = 1$ and $y = 8$ into the inequality: $8 < 2(1)^2 + 3(1) - 5$ $8 < 2(1) + 3 - 5$ $8 < 2 + 3 - 5$ $8 < 0 \quad \text{(False)}$ So, point $(1, 8)$ is not a solution.

3. Point $(-5, 10)$:

Substitute $x = -5$ and $y = 10$ into the inequality: $10 < 2(-5)^2 + 3(-5) - 5$ $10 < 2(25) - 15 - 5$ $10 < 50 - 15 - 5$ $10 < 30 \quad \text{(True)}$ So, point $(-5, 10)$ is a solution.

4. Point $(3, 6)$:

Substitute $x = 3$ and $y = 6$ into the inequality: $6 < 2(3)^2 + 3(3) - 5$ $6 < 2(9) + 9 - 5$ $6 < 18 + 9 - 5$ $6 < 22 \quad \text{(True)}$ So, point $(3, 6)$ is a solution.

5. Point $(-3, 4)$:

Substitute $x = -3$ and $y = 4$ into the inequality: $4 < 2(-3)^2 + 3(-3) - 5$ $4 < 2(9) - 9 - 5$ $4 < 18 - 9 - 5$ $4 < 4 \quad \text{(False)}$ So, point $(-3, 4)$ is not a solution.

6. Point $(2, 9)$:

Substitute $x = 2$ and $y = 9$ into the inequality: $9 < 2(2)^2 + 3(2) - 5$ $9 < 2(4) + 6 - 5$ $9 < 8 + 6 - 5$ $9 < 9 \quad \text{(False)}$ So, point $(2, 9)$ is not a solution.

Summary of Results:

1. $(1, 8)$: False
2. $(-5, 10)$: True
3. $(3, 6)$: True
4. $(-3, 4)$: False
5. $(2, 9)$: False

Do you want more details or have any questions?

Here are 5 related questions:

1. How do we solve a quadratic inequality like $y < 2x^2 + 3x - 5$?
2. What is the significance of the boundary curve $y = 2x^2 + 3x - 5$?
3. How can we graphically check the solutions to this inequality?
4. What does it mean for a point to lie "inside" or "outside" the solution region?
5. How would the solution change if the inequality were $y \leq 2x^2 + 3x - 5$?

Tip: Always check if your quadratic inequality has been simplified properly before substituting points.