Question

Which of the following coordinate pairs is a point on the parabola y=-4x^ 2 -53x-56?; (- 4, - 56); (- 1, - 7); (- 4, 220); (- 1, 13)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if a coordinate pair is a point on the given parabola, we substitute the x-value into the equation and check if the resulting y-value matches the given y-value.

Let's check each coordinate pair:

1. (-4, -56):
Substituting x = -4 into the equation y = -4x^2 - 53x - 56:
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 92
The y-value does not match -56, so (-4, -56) is not a point on the parabola.

2. (-1, -7):
Substituting x = -1:
y = -4(-1)^2 - 53(-1) - 56
y = -4(1) + 53 - 56
y = -4 + 53 - 56
y = -7
The y-value matches -7, so (-1, -7) is a point on the parabola.

3. (-4, 220):
Substituting x = -4:
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 92
The y-value does not match 220, so (-4, 220) is not a point on the parabola.

4. (-1, 13):
Substituting x = -1:
y = -4(-1)^2 - 53(-1) - 56
y = -4(1) + 53 - 56
y = -4 + 53 - 56
y = -7
The y-value does not match 13, so (-1, 13) is not a point on the parabola.

Therefore, the only point on the parabola y = -4x^2 - 53x - 56 is (-1, -7).