Question

Which of the following coordinate pairs is a point on the parabola y=2x2−24x−15

?(1 point)
Responses

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

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

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

(−11,7)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To check if a coordinate pair is a point on the parabola, we substitute the x-value into the equation for x and see if it equals the y-value.

Let's check each of the options:

1) (11, -37):
y = 2(11)^2 - 24(11) - 15 = 242 - 264 - 15 = -37. This matches the y-value, so (11, -37) is a point on the parabola.

2) (2, -15):
y = 2(2)^2 - 24(2) - 15 = 8 - 48 - 15 = -55. This doesn't match the y-value, so (2, -15) is not a point on the parabola.

3) (2, -47):
y = 2(2)^2 - 24(2) - 15 = 8 - 48 - 15 = -55. This doesn't match the y-value, so (2, -47) is not a point on the parabola.

4) (-11, 7):
y = 2(-11)^2 - 24(-11) - 15 = 242 + 264 - 15 = 491. This doesn't match the y-value, so (-11, 7) is not a point on the parabola.

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

Answer 2

[AI-generated answer — Explain Bot]

To determine which coordinate pair is a point on the parabola, we need to substitute the x-value from each pair into the equation and check if it satisfies the equation.

Let's calculate using each coordinate pair:

For the first coordinate pair, (11, -37):
Substituting x=11 into the equation:
y = 2(11)^2 - 24(11) - 15
y = 2(121) - 264 - 15
y = 242 - 264 - 15
y = -37

The y-value obtained (-37) matches the y-value in the coordinate pair, so (11, -37) is a point on the parabola.

For the second coordinate pair, (2, -15):
Substituting x=2 into the equation:
y = 2(2)^2 - 24(2) - 15
y = 2(4) - 48 - 15
y = 8 - 48 - 15
y = -55

The y-value obtained (-55) does not match the y-value in the coordinate pair, so (2, -15) is not a point on the parabola.

For the third coordinate pair, (2, -47):
Substituting x=2 into the equation:
y = 2(2)^2 - 24(2) - 15
y = 2(4) - 48 - 15
y = 8 - 48 - 15
y = -55

The y-value obtained (-55) does not match the y-value in the coordinate pair, so (2, -47) is not a point on the parabola.

For the fourth coordinate pair, (-11, 7):
Substituting x=-11 into the equation:
y = 2(-11)^2 - 24(-11) - 15
y = 2(121) + 264 - 15
y = 242 + 264 - 15
y = 491

The y-value obtained (491) does not match the y-value in the coordinate pair, so (-11, 7) is not a point on the parabola.

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

Answer 3

[AI-generated answer — Step-by-Step Bot]

To determine if a given coordinate pair is a point on the parabola y=2x^2−24x−15, we substitute the x and y values into the equation and check if it is satisfied.

Let's try each coordinate pair:

1. For (11, −37):
Substituting x=11 and y=−37 into the equation:
−37 = 2(11^2) − 24(11) − 15
−37 = 242 − 264 − 15
−37 = −37

Since the equation is true, (11, −37) is a point on the parabola.

2. For (2, −15):
Substituting x=2 and y=−15 into the equation:
−15 = 2(2^2) − 24(2) − 15
−15 = 8 − 48 − 15
−15 = −55

Since the equation is not true, (2, −15) is not a point on the parabola.

3. For (2, −47):
Substituting x=2 and y=−47 into the equation:
−47 = 2(2^2) − 24(2) − 15
−47 = 8 − 48 − 15
−47 = −55

Since the equation is not true, (2, −47) is not a point on the parabola.

4. For (−11, 7):
Substituting x=−11 and y=7 into the equation:
7 = 2(−11^2) − 24(−11) − 15
7 = 242 + 264 − 15
7 = 491

Since the equation is not true, (−11, 7) is not a point on the parabola.

Therefore, the coordinate pair that is a point on the parabola y=2x^2−24x−15 is (11, −37).