Question

Which of the following coordinate pairs is a point on the parabola y=−4x^2−53x−56 ?(1 point)
Responses

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

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

(−4,220)
left parenthesis negative 4 comma 220 right parenthesis

(−1,13)

Answer 1

that's not correct

Answer 2

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

Let's evaluate each pair:

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

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

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

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

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

Answer 3

Let's carefully reevaluate each of the coordinate pairs provided against the equation of the parabola \( y = -4x^2 - 53x - 56 \).

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

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

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

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

Based on these computations:

- The point \((-1, -7)\) is indeed correct,
- The points \((-4, -56)\) and \((-4, 220)\) do not satisfy the equation, and
- The point \((-1, 13)\) is also not correct.

If you have any specific details or corrections in mind regarding the points or the calculation, please let me know so I can assist you appropriately!