Question

Which coordinate pair is a a point on the parabola y=2x^2−24x−15
(1 point)
Responses

(−11, 7)
(−11, 7)

(2, −15)
(2, −15)

(2, −47)
(2, −47)

(11, −37)

Answer 1

To determine which coordinate pair is a point on the parabola defined by the equation \( y = 2x^2 - 24x - 15 \), you need to substitute the \( x \)-value from each coordinate pair into the equation and see if the resulting \( y \) value matches the \( y \)-value given in the coordinate pair.

Let's evaluate each pair:

1. **For (-11, 7)**:
\[
y = 2(-11)^2 - 24(-11) - 15 = 2(121) + 264 - 15 = 242 + 264 - 15 = 491 \quad (\text{not 7})
\]

2. **For (2, -15)**:
\[
y = 2(2)^2 - 24(2) - 15 = 2(4) - 48 - 15 = 8 - 48 - 15 = 8 - 63 = -55 \quad (\text{not -15})
\]

3. **For (2, -47)**:
\[
y = 2(2)^2 - 24(2) - 15 = 2(4) - 48 - 15 = 8 - 48 - 15 = 8 - 63 = -55 \quad (\text{not -47})
\]

4. **For (11, -37)**:
\[
y = 2(11)^2 - 24(11) - 15 = 2(121) - 264 - 15 = 242 - 264 - 15 = 242 - 279 = -37 \quad (\text{is -37})
\]

The coordinate pair \( (11, -37) \) is a point on the parabola \( y = 2x^2 - 24x - 15 \).