Which of the following coordinate pairs is a point on the parabola y=−4x2−53x−56

Question

?(1 point)
Responses

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

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

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

(−4,220)

Answer 1

To determine which of the given pairs is a point on the parabola represented by the equation \( y = -4x^2 - 53x - 56 \), we need to substitute the x-values from the coordinate pairs into the equation and check if the resulting y-value matches the y-value in the coordinate pair.

1. For the point \((-1, -7)\): \[ y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -7 \] This point is on the parabola.

2. For the point \((-4, -56)\): \[ y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = 92 \] This point is not on the parabola.

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

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

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

\((-1, -7)\)