Question

Which of the following is a point you can generate to create the parabola for the quadratic equation y = -6x^2 + 3x + 8
.

Answer 1

To generate points for the parabola given by the quadratic equation \( y = -6x^2 + 3x + 8 \), you can select various values for \( x \) and calculate the corresponding \( y \) values.

Here are a few points you can generate:

1. **For \( x = 0 \)**:
\[
y = -6(0)^2 + 3(0) + 8 = 8
\]
Point: \( (0, 8) \)

2. **For \( x = 1 \)**:
\[
y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5
\]
Point: \( (1, 5) \)

3. **For \( x = -1 \)**:
\[
y = -6(-1)^2 + 3(-1) + 8 = -6 - 3 + 8 = -1
\]
Point: \( (-1, -1) \)

4. **For \( x = \frac{1}{2} \)**:
\[
y = -6\left(\frac{1}{2}\right)^2 + 3\left(\frac{1}{2}\right) + 8 = -6\left(\frac{1}{4}\right) + \frac{3}{2} + 8 = -\frac{3}{2} + \frac{3}{2} + 8 = 8
\]
Point: \( \left(\frac{1}{2}, 8\right) \)

5. **For \( x = 2 \)**:
\[
y = -6(2)^2 + 3(2) + 8 = -24 + 6 + 8 = -10
\]
Point: \( (2, -10) \)

By calculating \( y \) for these \( x \) values, you can generate the following points on the parabola: \( (0, 8) \), \( (1, 5) \), \( (-1, -1) \), \( \left(\frac{1}{2}, 8\right) \), and \( (2, -10) \). You can choose any of these points to help create the graph of the parabola.