Which of the following coordinate pairs is a point on the parabola y=−4x2−53x−56 ?(1 point) Responses (−4,−56) left parenthesis negative 4 comma negative 56 right parenthesis (−1,−7) left parenthesis negative1 comma negative 7 right parenthesis (−4,220) left parenthesis negative 4 comma 220 right parenthesis (−1,13)

1 answer

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

  1. Check the point \((-4, -56)\): \[ y = -4(-4)^2 - 53(-4) - 56 \] \[ = -4(16) + 212 - 56 \] \[ = -64 + 212 - 56 = 92 \quad (\text{not } -56) \]

  2. Check the point \((-1, -7)\): \[ y = -4(-1)^2 - 53(-1) - 56 \] \[ = -4(1) + 53 - 56 \] \[ = -4 + 53 - 56 = -7 \quad (\text{matches } -7) \]

  3. Check the point \((-4, 220)\): \[ y = -4(-4)^2 - 53(-4) - 56 \] (We calculated this earlier and found it to be 92, not 220.) \[ = 92 \quad (\text{not } 220) \]

  4. Check the point \((-1, 13)\): \[ y = -4(-1)^2 - 53(-1) - 56 \] (We calculated this earlier and found it to be -7, not 13.) \[ = -7 \quad (\text{not } 13) \]

The only coordinate pair that is a point on the parabola is \((-1, -7)\).