Question

y=-2x 2-8x-7 (-2, -1) solution set for equation

(-2, -1)

(-1, -1)
(-1, -1)

(0, 7)
(0, 7)

(2, 31)
(2, 31)

(-1, -17)

Answer 1

To find out if the points given are solutions of the equation \( y = -2x^2 - 8x - 7 \), we can substitute the x-values of the points into the equation and see if we get the corresponding y-values.

The equation is:

\[
y = -2x^2 - 8x - 7
\]

Let's test each of the points:

1. **Point (-2, -1)**:
\[
y = -2(-2)^2 - 8(-2) - 7 = -2(4) + 16 - 7 = -8 + 16 - 7 = 1 \quad \text{(Not a solution)}
\]

2. **Point (-1, -1)**:
\[
y = -2(-1)^2 - 8(-1) - 7 = -2(1) + 8 - 7 = -2 + 8 - 7 = -1 \quad \text{(A solution)}
\]

3. **Point (0, 7)**:
\[
y = -2(0)^2 - 8(0) - 7 = -2(0) - 0 - 7 = -7 \quad \text{(Not a solution)}
\]

4. **Point (2, 31)**:
\[
y = -2(2)^2 - 8(2) - 7 = -2(4) - 16 - 7 = -8 - 16 - 7 = -31 \quad \text{(Not a solution)}
\]

5. **Point (-1, -17)**:
\[
y = -2(-1)^2 - 8(-1) - 7 = -2(1) + 8 - 7 = -2 + 8 - 7 = -1 \quad \text{(Not a solution)}
\]

### Summary of Results:
- (-2, -1): Not a solution
- (-1, -1): A solution
- (0, 7): Not a solution
- (2, 31): Not a solution
- (-1, -17): Not a solution

Thus, the only point that is a solution to the equation \( y = -2x^2 - 8x - 7 \) is **(-1, -1)**.