Question

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

A: ( -6, 206)

B: ( -3, 323)

C: ( -6 , 8)

D: ( -3, -55)

Answer 1

To determine if any of the given options is a point on the parabola described by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can evaluate the equation for each of the x-coordinates provided in the options, and check if the corresponding y-value matches.

1. **Option A: ( -6, 206)**
\[
y = -6(-6)^2 + 3(-6) + 8
\]
\[
= -6(36) - 18 + 8
\]
\[
= -216 - 18 + 8
\]
\[
= -226 \quad (\text{not } 206)
\]

2. **Option B: ( -3, 323)**
\[
y = -6(-3)^2 + 3(-3) + 8
\]
\[
= -6(9) - 9 + 8
\]
\[
= -54 - 9 + 8
\]
\[
= -55 \quad (\text{not } 323)
\]

3. **Option C: ( -6, 8)**
\[
y = -6(-6)^2 + 3(-6) + 8
\]
\[
= -6(36) - 18 + 8
\]
\[
= -216 - 18 + 8
\]
\[
= -226 \quad (\text{not } 8)
\]

4. **Option D: ( -3, -55)**
\[
y = -6(-3)^2 + 3(-3) + 8
\]
\[
= -6(9) - 9 + 8
\]
\[
= -54 - 9 + 8
\]
\[
= -55 \quad (\text{matches -55})
\]

The point that satisfies the quadratic equation \( y = -6x^2 + 3x + 8 \) is **D: (-3, -55)**.