Question

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


(1 point)
Responses

(-4, 220)
(-4, 220)

(-1, 13)
(-1, 13)

(-4, -56)
(-4, -56)

(-1, -7)

Answer 1

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

1. For the point \((-4, 220)\):

\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
= -4(16) + 212 - 56
\]
\[
= -64 + 212 - 56
\]
\[
= 92 \quad \text{(not } 220\text{)}
\]

2. For the point \((-1, 13)\):

\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
= -4(1) + 53 - 56
\]
\[
= -4 + 53 - 56
\]
\[
= -7 \quad \text{(not } 13\text{)}
\]

3. For the point \((-4, -56)\):

\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
= -4(16) + 212 - 56
\]
\[
= -64 + 212 - 56
\]
\[
= 92 \quad \text{(not } -56\text{)}
\]

4. For the point \((-1, -7)\):

\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
= -4(1) + 53 - 56
\]
\[
= -4 + 53 - 56
\]
\[
= -7 \quad \text{(this matches } -7\text{)}
\]

The correct coordinate pair that lies on the parabola \( y = -4x^2 - 53x - 56 \) is:

\[\boxed{(-1, -7)}\]