Question

Which of the following coordinate pairs is a point on the parabola y=−4x2−53x−56

(1 point)
Responses

(-4, 220)
(-4, 220)

(-1, -7)
(-1, -7)

(-1, 13)
(-1, 13)

(-4, -56)

Answer 1

To determine which coordinate pair is a point on the parabola defined by the equation \( y = -4x^2 - 53x - 56 \), we need to substitute the x-coordinate of each pair into the equation and see if it gives the corresponding y-coordinate.

1. **For the pair (-4, 220)**:
\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
y = -4(16) + 212 - 56
\]
\[
y = -64 + 212 - 56 = 92 \quad \text{(not 220)}
\]

2. **For the pair (-1, -7)**:
\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
y = -4(1) + 53 - 56
\]
\[
y = -4 + 53 - 56 = -7 \quad \text{(matches)}
\]

3. **For the pair (-1, 13)**:
\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
y = -4(1) + 53 - 56
\]
\[
y = -4 + 53 - 56 = -7 \quad \text{(not 13)}
\]

4. **For the pair (-4, -56)**:
\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
y = -4(16) + 212 - 56
\]
\[
y = -64 + 212 - 56 = 92 \quad \text{(not -56)}
\]

The only coordinate pair that satisfies the equation of the parabola is **(-1, -7)**. Therefore, that is the point on the parabola.