Question

A) Which of the following coordinate pairs is a point on the parabola y = 2x
2 − 24x − 15?
(1 point)
(11, − 37)
(2, − 15)
(2, − 47)
(−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 need to substitute each x-value from the coordinate pairs into the equation and check if the resulting y-value matches the one given in the pair.

The equation is:
\[
y = 2x^2 - 24x - 15
\]

Let's calculate \( y \) for each x in the pairs:

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

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

3. **For (2, −47)**:
\[
y = 2(2)^2 - 24(2) - 15
\]
As we already calculated above, \( y = -55 \quad \text{(does not match)} \)

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

Therefore, the only coordinate pair that lies on the parabola \( y = 2x^2 - 24x - 15 \) is **(11, −37)**.