Question
6. 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
the parabola 𝑦 = 2𝑥
2 − 24𝑥 − 15
(-11, 7)
(2, -47)
(11, -37)
(2, -15
Answers
GPT-4o mini
To determine which of the provided coordinate pairs is a point on the parabola described by the equation \( y = 2x^2 - 24x - 15 \), we can substitute each \( x \) value from the pairs into the equation to see if the resulting \( y \) value matches.
1. For the point (-11, 7):
\[
y = 2(-11)^2 - 24(-11) - 15
\]
\[
= 2(121) + 264 - 15
\]
\[
= 242 + 264 - 15 = 491
\]
Since \( 491 \neq 7 \), this point is not on the parabola.
2. For the point (2, -47):
\[
y = 2(2)^2 - 24(2) - 15
\]
\[
= 2(4) - 48 - 15
\]
\[
= 8 - 48 - 15 = -55
\]
Since \( -55 \neq -47 \), this point is not on the parabola.
3. For the point (11, -37):
\[
y = 2(11)^2 - 24(11) - 15
\]
\[
= 2(121) - 264 - 15
\]
\[
= 242 - 264 - 15 = -37
\]
Since \( -37 = -37 \), this point is on the parabola.
4. For the point (2, -15):
\[
y = 2(2)^2 - 24(2) - 15
\]
This was calculated previously, yielding \( -55 \), so this point is also not on the parabola.
The only coordinate pair that is a point on the parabola is **(11, -37)**.
1. For the point (-11, 7):
\[
y = 2(-11)^2 - 24(-11) - 15
\]
\[
= 2(121) + 264 - 15
\]
\[
= 242 + 264 - 15 = 491
\]
Since \( 491 \neq 7 \), this point is not on the parabola.
2. For the point (2, -47):
\[
y = 2(2)^2 - 24(2) - 15
\]
\[
= 2(4) - 48 - 15
\]
\[
= 8 - 48 - 15 = -55
\]
Since \( -55 \neq -47 \), this point is not on the parabola.
3. For the point (11, -37):
\[
y = 2(11)^2 - 24(11) - 15
\]
\[
= 2(121) - 264 - 15
\]
\[
= 242 - 264 - 15 = -37
\]
Since \( -37 = -37 \), this point is on the parabola.
4. For the point (2, -15):
\[
y = 2(2)^2 - 24(2) - 15
\]
This was calculated previously, yielding \( -55 \), so this point is also not on the parabola.
The only coordinate pair that is a point on the parabola is **(11, -37)**.