Question

Which of the following coordinate pairs is a point on the parabola y=−4x2−53x−56
?(1 point)
Responses

(−1, 13)
(−1, 13)

(−4, 220)
(−4, 220)

(−4,−56)
open paren negative 4 comma negative 56 close paren

(−1,−7)

Answer 1

To determine which of the given coordinate pairs lies on the parabola defined by the equation \( y = -4x^2 - 53x - 56 \), we need to substitute the x-coordinate of each pair into the equation and see if the resulting y-value matches the y-coordinate of the pair.

1. **For the point (−1, 13)**:
\[
y = -4(-1)^2 - 53(-1) - 56
= -4(1) + 53 - 56
= -4 + 53 - 56
= -4 + -3
= -7 \quad \text{(not a match)}
\]

2. **For the point (−4, 220)**:
\[
y = -4(-4)^2 - 53(-4) - 56
= -4(16) + 212 - 56
= -64 + 212 - 56
= -64 + 156
= 92 \quad \text{(not a match)}
\]

3. **For the point (−4, −56)**:
\[
y = -4(-4)^2 - 53(-4) - 56
= -4(16) + 212 - 56
= -64 + 212 - 56
= -64 + 156
= 92 \quad \text{(not a match)}
\]

4. **For the point (−1, −7)**:
\[
y = -4(-1)^2 - 53(-1) - 56
= -4(1) + 53 - 56
= -4 + 53 - 56
= -4 + -3
= -7 \quad \text{(this is a match)}
\]

So, the point that lies on the parabola \( y = -4x^2 - 53x - 56 \) is **(−1, −7)**.