Question

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

(−1,13)
left parenthesis neagtive 1 comma 13 right parenthesis

(−1,−7)
left parenthesis negative1 comma negative 7 right parenthesis

(−4,−56)
left parenthesis negative 4 comma negative 56 right parenthesis

(−4,220)

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 need to substitute the x-coordinate of each point into the equation and see if the resulting y-coordinate matches.

1. **For \((-1, 13)\)**:
\[
y = -4(-1)^2 - 53(-1) - 56
= -4(1) + 53 - 56
= -4 + 53 - 56
= -4 + 53 - 56
= -4 + (53 - 56)
= -4 - 3
= -7 \quad \text{(not 13, so this point does not lie on the parabola)}
\]

2. **For \((-1, -7)\)**:
\[
y = -4(-1)^2 - 53(-1) - 56
= -4(1) + 53 - 56
= -4 + 53 - 56
= -4 + 53 - 56
= -4 - 3
= -7 \quad \text{(this matches, so this point lies on the parabola)}
\]

3. **For \((-4, -56)\)**:
\[
y = -4(-4)^2 - 53(-4) - 56
= -4(16) + 212 - 56
= -64 + 212 - 56
= -64 + 156
= 92 \quad \text{(not -56, so this point does not lie on the parabola)}
\]

4. **For \((-4, 220)\)**:
\[
y = -4(-4)^2 - 53(-4) - 56
= -4(16) + 212 - 56
= -64 + 212 - 56
= -64 + 156
= 92 \quad \text{(not 220, so this point does not lie on the parabola)}
\]

Thus, the only point that lies on the parabola \( y = -4x^2 - 53x - 56 \) is:

\((-1, -7)\).