Question

Which of the following coordinate pairs is a point on the parabola y=−4x2−53x−56?(1 point) Responses (−4,−56) left parenthesis negative 4 comma negative 56 right parenthesis (−4,220) left parenthesis negative 4 comma 220 right parenthesis (−1,13) left parenthesis neagtive 1 comma 13 right parenthesis (−1,−7)

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 will plug in the x-coordinates from each pair into the equation and see if the resulting \( y \) value matches the y-coordinate from the pair.

1. **For (-4, -56)**:
\[
y = -4(-4)^2 - 53(-4) - 56
= -4(16) + 212 - 56
= -64 + 212 - 56
= 92
\]
The point is (-4, 92), not (-4, -56).

2. **For (-4, 220)**:
\[
y = -4(-4)^2 - 53(-4) - 56
= -4(16) + 212 - 56
= -64 + 212 - 56
= 92
\]
The point is (-4, 92), not (-4, 220).

3. **For (-1, 13)**:
\[
y = -4(-1)^2 - 53(-1) - 56
= -4(1) + 53 - 56
= -4 + 53 - 56
= -7
\]
The point is (-1, -7), not (-1, 13).

4. **For (-1, -7)**:
\[
y = -4(-1)^2 - 53(-1) - 56
= -4(1) + 53 - 56
= -4 + 53 - 56
= -7
\]
The point is (-1, -7), which matches.

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