Question

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)

Answer 1

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

1. **For \((-11, 7)\)**:
\( x = -11 \)
\[
y = 2(-11)^2 - 24(-11) - 15 = 2(121) + 264 - 15 = 242 + 264 - 15 = 491
\]
\( y \neq 7 \)

2. **For \( (2, -47) \)**:
\( x = 2 \)
\[
y = 2(2)^2 - 24(2) - 15 = 2(4) - 48 - 15 = 8 - 48 - 15 = -55
\]
\( y \neq -47 \)

3. **For \( (11, -37) \)**:
\( x = 11 \)
\[
y = 2(11)^2 - 24(11) - 15 = 2(121) - 264 - 15 = 242 - 264 - 15 = -37
\]
\( y = -37 \)

4. **For \( (2, -15) \)**:
\( x = 2 \)
\[
y = 2(2)^2 - 24(2) - 15 = 2(4) - 48 - 15 = 8 - 48 - 15 = -55
\]
\( y \neq -15 \)

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

Answer 2

Please make it shorter

Answer 3

To check which coordinate pair lies on the parabola \(y = 2x^2 - 24x - 15\):

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

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

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

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

The pair that lies on the parabola is \((11, -37)\).

Answer 4

shorter please

Answer 5

To verify which point lies on the parabola \(y = 2x^2 - 24x - 15\):

1. \((-11, 7)\): \(y = 491\) (not \(7\))
2. \((2, -47)\): \(y = -55\) (not \(-47\))
3. \((11, -37)\): \(y = -37\) (matches)
4. \((2, -15)\): \(y = -55\) (not \(-15\))

**Point on the parabola:** \((11, -37)\).