Question

Which of the following is a point you can generate to create the parabola for the quadratic equation y=−6x2+3x+8 ?(1 point)
Responses

(−6,206)
left parenthesis negative 6 comma 206 right parentheis

(−3,−55)
left parenthesis negative 3 comma negative 55 right parentheis

(−6,8)
left parenthesis negative 6 comma 8 right parentheis

(−3,323)

Answer 1

To determine which of the points can be generated to create the parabola for the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute each point into the equation and see if it satisfies the equation (i.e., if the left-hand side equals the right-hand side).

Let's check each point:

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

2. **For \((-3, -55)\)**:
\[
y = -6(-3)^2 + 3(-3) + 8
\]
\[
= -6(9) - 9 + 8
\]
\[
= -54 - 9 + 8 = -55 \quad \text{(this point works)}
\]

3. **For \((-6, 8)\)**:
\[
y = -6(-6)^2 + 3(-6) + 8
\]
This calculation is the same as the first point, which we already evaluated to be:
\[
= -226 \quad \text{(not } 8\text{)}
\]

4. **For \((-3, 323)\)**:
\[
y = -6(-3)^2 + 3(-3) + 8
\]
As we calculated before, this gives us:
\[
= -55 \quad \text{(not } 323\text{)}
\]

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

Thus, the correct response is:
**\((-3, -55)\)**.