which of the following coordinate pairs is a point on the parabola y=-4x^2-53x-56?
(-4, 220)
(-1, -7)
(-1, 13)
(-4, -56)
To determine if a coordinate pair is a point on the parabola, we substitute the x-value into the equation and check if the resulting y-value is equal to the given y-value.
For the coordinate pair (-4, 220):
y = -4x^2 - 53x - 56
220 = -4(-4)^2 - 53(-4) - 56
220 = -4(16) + 212 - 56
220 = -64 + 212 - 56
220 = 148. The resulting y-value does not equal 220, so (-4, 220) is not a point on the parabola.
For the coordinate pair (-1, -7):
y = -4(-1)^2 - 53(-1) - 56
-7 = -4(1) + 53 - 56
-7 = -4 + 53 - 56
-7 = -4 - 3. The resulting y-value does equal -7, so (-1, -7) is a point on the parabola.
For the coordinate pair (-1, 13):
y = -4(-1)^2 - 53(-1) - 56
13 = -4(1) + 53 - 56
13 = -4 + 53 - 56
13 = -4 - 3. The resulting y-value does not equal 13, so (-1, 13) is not a point on the parabola.
For the coordinate pair (-4, -56):
y = -4(-4)^2 - 53(-4) - 56
-56 = -4(16) + 212 - 56
-56 = -64 + 212 - 56
-56 = -56. The resulting y-value does equal -56, so (-4, -56) is a point on the parabola.
The point on the parabola is (-1, -7).