Which of the following coordinate pairs is a point on the parabola

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 \( x \)-values of the coordinate pairs into the equation and see if the resulting \( y \)-values match.

Let's evaluate each coordinate pair one by one:

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

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

3. For the point \((-4, 220)\) (we already calculated \( y \) for \( x = -4 \)):
- We found \( y = 92 \), so this point does not satisfy the equation.

4. For the point \((-1, -7)\):
- We determined that when \( x = -1 \), \( y = -7 \).

Since \((-1, -7)\) matched our calculation, we can conclude:

The coordinate pair that is a point on the parabola \( y = -4x^2 - 53x - 56 \) is **(-1, -7)**.