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

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

1. For the point \((-4, -56)\):
\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
= -4(16) + 212 - 56
\]
\[
= -64 + 212 - 56
\]
\[
= 92 \quad (\text{not } -56)
\]

2. For the point \((-1, -7)\):
\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
= -4(1) + 53 - 56
\]
\[
= -4 + 53 - 56
\]
\[
= -7 \quad (\text{this is the same as } -7)
\]

3. For the point \((-4, 220)\):
\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
= -4(16) + 212 - 56
\]
\[
= -64 + 212 - 56
\]
\[
= 92 \quad (\text{not } 220)
\]

4. For the point \((-1, 13)\):
\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
= -4(1) + 53 - 56
\]
\[
= -4 + 53 - 56
\]
\[
= -7 \quad (\text{not } 13)
\]

After checking all the coordinate pairs, we find that the point \((-1, -7)\) is indeed a point on the parabola \( y = -4x^2 - 53x - 56 \).

Thus, the answer is:
\(\boxed{(-1, -7)}\)