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 to create the parabola for the quadratic equation \( y = -6x^2 + 3x + 8 \), you can choose different values for \( x \) and calculate the corresponding \( y \) values. Here are a few values of \( x \) and their corresponding \( y \):

1. **When \( x = 0 \):**
\[
y = -6(0)^2 + 3(0) + 8 = 8 \quad \text{(Point: (0, 8))}
\]

2. **When \( x = 1 \):**
\[
y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5 \quad \text{(Point: (1, 5))}
\]

3. **When \( x = -1 \):**
\[
y = -6(-1)^2 + 3(-1) + 8 = -6 - 3 + 8 = -1 \quad \text{(Point: (-1, -1))}
\]

4. **When \( x = 2 \):**
\[
y = -6(2)^2 + 3(2) + 8 = -24 + 6 + 8 = -10 \quad \text{(Point: (2, -10))}
\]

5. **When \( x = -2 \):**
\[
y = -6(-2)^2 + 3(-2) + 8 = -24 - 6 + 8 = -22 \quad \text{(Point: (-2, -22))}
\]

You can continue to calculate more points to get a better graph of the parabola. The points generated above include:

1. (0, 8)
2. (1, 5)
3. (-1, -1)
4. (2, -10)
5. (-2, -22)

These points should help in plotting the parabola defined by the quadratic equation.