Which of the following coordinate pairs is a point on the parabola y=−4x2−53x−56
?
(1 point)
Responses
(-4,-56)
(-4,-56)
(-1,-7)
(-1,-7)
(-4,220)
(-4,220)
(-1,13)
To determine if a point is on the parabola, we substitute the x-coordinate of the point into the equation and check if the resulting y-coordinate matches the given y-coordinate.
Let's check each option:
1. For (-4, -56):
Substituting x = -4 into the equation:
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 156 - 56
y = -64 + 100
y = 36
The resulting y-coordinate is 36, which does not match the given y-coordinate of -56.
2. For (-1, -7):
Substituting x = -1 into the equation:
y = -4(-1)^2 - 53(-1) - 56
y = -4(1) + 53 - 56
y = -4 + 53 - 56
y = -60
The resulting y-coordinate is -60, which does not match the given y-coordinate of -7.
3. For (-4, 220):
Substituting x = -4 into the equation:
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 148
The resulting y-coordinate is 148, which does not match the given y-coordinate of 220.
4. For (-1, 13):
Substituting x = -1 into the equation:
y = -4(-1)^2 - 53(-1) - 56
y = -4(1) + 53 - 56
y = -4 + 53 - 56
y = -7
The resulting y-coordinate is -7, which matches the given y-coordinate of -7.
Therefore, the point (-1, 13) is on the parabola y = -4x^2 - 53x - 56.