Question

Which of the following coordinate pairs is a point on the parabola y=−4x2−53x−56 (1 point) Responses (-4, -56) (-1, -7) (-4, 220) (-1, 13)

Answer 1

To determine which of the coordinate pairs is a point on the parabola defined by the equation \( y = -4x^2 - 53x - 56 \), we can substitute the x-coordinate of each pair into the equation and see if we obtain the corresponding y-coordinate.

1. **For \((-4, -56)\)**:
\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
y = -4(16) + 212 - 56
\]
\[
y = -64 + 212 - 56 = 92 \; (\text{not } -56)
\]

2. **For \((-1, -7)\)**:
\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
y = -4(1) + 53 - 56
\]
\[
y = -4 + 53 - 56 = -7 \; (\text{matches})
\]

3. **For \((-4, 220)\)**:
\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
y = -4(16) + 212 - 56
\]
\[
y = -64 + 212 - 56 = 92 \; (\text{not } 220)
\]

4. **For \((-1, 13)\)**:
\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
y = -4(1) + 53 - 56
\]
\[
y = -4 + 53 - 56 = -7 \; (\text{not } 13)
\]

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