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



(1 point)
Responses

(-1, -7)
(-1, -7)

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

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

(-1, 13)

1 answer

To determine which coordinate pairs are points on the parabola defined by the equation \( y = -4x^2 - 53x - 56 \), we need to substitute the \( x \) values of each pair into the equation and see if the resulting \( y \) value matches the given \( y \) value.

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

  4. For 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.

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