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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

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

(−4,220)

1 answer

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

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

  2. For \( (-4, -56) \): \[ y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = 92 \] This gives us \( y = 92 \), which does not match \( -56 \).

  3. For \( (-1, 13) \): We already calculated \( y \) for \( x = -1 \) and found it to be \( -7 \), not \( 13 \).

  4. For \( (-4, 220) \): We already calculated \( y \) for \( x = -4 \) and found it to be \( 92 \), not \( 220 \).

From these calculations, the only pair that is a point on the parabola is:

\( (-1, -7) \)