Question

Which of the following coordinate pairs is a point on the parabola y=2x2−24x−15
?(1 point)
Responses

(2,−47)
left parenthesis 2 comma negative 47 right parenthesis

(2,−15)
left parenthesis 2 comma negative 15 right parenthesis

(11,−37)
left parenthesis 11 comma negative 37 right parenthesis

(−11,7)

Answer 1

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

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

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

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

4. For the point **(-11, 7)**:
\[
y = 2(-11)^2 - 24(-11) - 15 \\
= 2(121) + 264 - 15 \\
= 242 + 264 - 15 \\
= 506 - 15 \\
= 491 \quad (\text{not } 7)
\]

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