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Which of the following coordinate pairs is a point on the parabola y=2x^2-24x-15

(-11, 7)
(2, -47)
(11, -37)
(2, -15)

5 answers

To determine which of the given coordinate pairs is a point on the parabola described by the equation \( y = 2x^2 - 24x - 15 \), we will substitute the \( x \) values from each pair into the equation and see if we get the corresponding \( y \) value.

  1. For \((-11, 7)\): \( x = -11 \) \[ y = 2(-11)^2 - 24(-11) - 15 = 2(121) + 264 - 15 = 242 + 264 - 15 = 491 \] \( y \neq 7 \)

  2. For \( (2, -47) \): \( x = 2 \) \[ y = 2(2)^2 - 24(2) - 15 = 2(4) - 48 - 15 = 8 - 48 - 15 = -55 \] \( y \neq -47 \)

  3. For \( (11, -37) \): \( x = 11 \) \[ y = 2(11)^2 - 24(11) - 15 = 2(121) - 264 - 15 = 242 - 264 - 15 = -37 \] \( y = -37 \)

  4. For \( (2, -15) \): \( x = 2 \) \[ y = 2(2)^2 - 24(2) - 15 = 2(4) - 48 - 15 = 8 - 48 - 15 = -55 \] \( y \neq -15 \)

The only coordinate pair that is a point on the parabola is \((11, -37)\).

Please make it shorter

To check which coordinate pair lies on the parabola \(y = 2x^2 - 24x - 15\):

  1. For \((-11, 7)\): \[ y = 2(-11)^2 - 24(-11) - 15 = 491 \quad (\text{not } 7) \]

  2. For \((2, -47)\): \[ y = 2(2)^2 - 24(2) - 15 = -55 \quad (\text{not } -47) \]

  3. For \((11, -37)\): \[ y = 2(11)^2 - 24(11) - 15 = -37 \quad (\text{is } -37) \]

  4. For \((2, -15)\): \[ y = 2(2)^2 - 24(2) - 15 = -55 \quad (\text{not } -15) \]

The pair that lies on the parabola is \((11, -37)\).

shorter please

To verify which point lies on the parabola \(y = 2x^2 - 24x - 15\):

  1. \((-11, 7)\): \(y = 491\) (not \(7\))
  2. \((2, -47)\): \(y = -55\) (not \(-47\))
  3. \((11, -37)\): \(y = -37\) (matches)
  4. \((2, -15)\): \(y = -55\) (not \(-15\))

Point on the parabola: \((11, -37)\).