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 that create the parabola for the quadratic equation \( y = -6x^2 + 3x + 8 \), you can substitute various values of \( x \) into the equation to calculate the corresponding values of \( y \).

Here are a few examples of points you can generate:

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

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

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

4. **For \( x = 2 \)**:
\[
y = -6(2)^2 + 3(2) + 8 = -24 + 6 + 8 = -10
\]
So, the point is \( (2, -10) \).

These calculations show how to generate points, and any of these points can be used to plot the parabola defined by the given quadratic equation.