Question

Malik is graphing a parabola given by the equation y=−14x2+3x−6. Which table of ordered pairs would match this parabola?(1 point)Responsesx-valuey-value−2−6−6−10−10−6 x -value y -value negative 2 negative 6 negative 6 negative 10 negative 10 negative 6x-valuey-value2−16310−1x -value y -value 2 negative 1 6 3 10 negative 1x-valuey-value0−1−4−5−8−1 x -value y -value 0 negative 1 negative 4 negative 5 negative 8 negative 1x-valuey-value4−42−30−4

Answer 1

To determine which table of ordered pairs matches the given parabola \( y = -14x^2 + 3x - 6 \), we can evaluate the equation at various x-values and calculate the corresponding y-values. Let’s check the ordered pairs from the options provided and see if any match the outputs from the equation.

### Step 1: Calculate y-values for selected x-values
I will choose x-values and compute the corresponding y-values using the parabola equation.

1. **For \( x = -2 \)**:
\[
y = -14(-2)^2 + 3(-2) - 6 = -14(4) - 6 - 6 = -56 - 6 - 6 = -68
\]

2. **For \( x = -1 \)**:
\[
y = -14(-1)^2 + 3(-1) - 6 = -14(1) - 3 - 6 = -14 - 3 - 6 = -23
\]

3. **For \( x = 0 \)**:
\[
y = -14(0)^2 + 3(0) - 6 = -0 - 0 - 6 = -6
\]

4. **For \( x = 1 \)**:
\[
y = -14(1)^2 + 3(1) - 6 = -14(1) + 3 - 6 = -14 + 3 - 6 = -17
\]

5. **For \( x = 2 \)**:
\[
y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56
\]

### Step 2: Check the provided ordered pairs
Let's compare these computed values of y:

- \( x = -2 \): \( y = -68 \)
- \( x = -1 \): \( y = -23 \)
- \( x = 0 \): \( y = -6 \)
- \( x = 1 \): \( y = -17 \)
- \( x = 2 \): \( y = -56 \)

### Response Comparison
Let's break down each response you provided:

1. **Response 1**: \((-2, -6), (-6, -10), (-10, -6)\) - Not matching.
2. **Response 2**: \((2, -1), (6, 3), (10, -1)\) - Not matching.
3. **Response 3**: \((0, -1), (-4, -5), (-8, -1)\) - Not matching.
4. **Response 4**: \((4, -4), (2, -30), (-4, -1)\) - Not matching.

None of the provided tables of ordered pairs match with the calculated y-values from the parabola equation \( y = -14x^2 + 3x - 6 \).

### Conclusion
Based on the calculations and the pairs given, it seems like there might be an error in the provided ordered pairs—they do not correspond to the values of y calculated from the parabola equation.