Question

Which of the following coordinate pairs is a point on the parabola y=−4x^2−53x−56?

(1 point)
Responses

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

(-4, -56)
(-4, -56)

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

(-1, 13)

Answer 1

To determine which of the coordinate pairs is a point on the parabola given by the equation \( y = -4x^2 - 53x - 56 \), we can substitute the x-coordinates from each pair into the equation and check if the resulting y-coordinate matches that of the point.

1. For \((-1, -7)\):
\[
y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -7
\]
This point does satisfy the equation.

2. For \((-4, -56)\):
\[
y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = 92
\]
This point does not satisfy the equation.

3. For \((-4, 220)\):
\[
y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = 92
\]
This point does not satisfy the equation.

4. For \((-1, 13)\):
\[
y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -7
\]
This point does not satisfy the equation.

Thus, the only point that satisfies the equation \( y = -4x^2 - 53x - 56 \) is \((-1, -7)\).

**Answer: (-1, -7)**