Question

Which of the following is a point you can generate to create the parabola for the quadratic equation y=-6x^2+3x=8?
(-6, 8)
(-6, 206)
(-3, -55)
(-3, 323)

Answer 1

To determine which point can be generated from the quadratic equation \( y = -6x^2 + 3x + 8 \), we need to compute the value of \( y \) for various values of \( x \).

First, let's express the equation clearly:

\[ y = -6x^2 + 3x + 8 \]

Now, we can evaluate \( y \) for \( x = -6 \) and \( x = -3 \).

1. **For \( x = -6 \)**:

\[
y = -6(-6)^2 + 3(-6) + 8
\]
\[
= -6(36) - 18 + 8
\]
\[
= -216 - 18 + 8
\]
\[
= -216 - 10
\]
\[
= -226
\]

So, the point for \( x = -6 \) is \( (-6, -226) \), which does not match either of the choices.

2. **For \( x = -3 \)**:

\[
y = -6(-3)^2 + 3(-3) + 8
\]
\[
= -6(9) - 9 + 8
\]
\[
= -54 - 9 + 8
\]
\[
= -54 - 1
\]
\[
= -55
\]

So, the point for \( x = -3 \) is \( (-3, -55) \), which matches one of the given choices.

Thus, the correct answer is:

**(-3, -55)**