Question

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

(1 point)
Responses

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

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

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

(-4,-56)

Answer 1

To find points on the parabola, we need to substitute the x-coordinate into the equation and solve for the y-coordinate.

Let's check each coordinate pair:

For (-1,13):
y = -4(-1)^2 - 53(-1) - 56
y = -4 + 53 - 56
y = -7

The y-coordinate does not match, so (-1, 13) is not a point on the parabola.

For (-4,220):
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 92

The y-coordinate does not match, so (-4, 220) is not a point on the parabola.

For (-1,-7):
y = -4(-1)^2 - 53(-1) - 56
y = -4 + 53 - 56
y = -7

The y-coordinate matches, so (-1, -7) is a point on the parabola.

For (-4,-56):
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 92

The y-coordinate does not match, so (-4, -56) is not a point on the parabola.

Therefore, the only correct answer is (-1, -7).