Question

Which of the following is a point you can generate to create the parabola for the quadratic equation y=−6x2+3x+8
𝑦
=
−
6
𝑥
2
+
3
𝑥
+
8
?(1 point)
Responses

(−3,323)
(
−
3
,
323
)
left parenthesis negative 3 comma 323 right parentheis

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

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

(−6,206)

Answer 1

To determine a point that lies on the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the \( x \)-values from the given options into the equation and see which one yields the corresponding \( y \)-value.

Let's check each point:

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

2. **For (−3, −55)**:
We already calculated that \( y = -55 \) for \( x = -3 \), so this point is valid.

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

4. **For (−6, 206)**:
\[
y = -6(-6)^2 + 3(-6) + 8
\]
We already calculated that \( y = -226 \) for \( x = -6 \), so this point does not hold.

Thus, the only correct point that lies on the parabola is:
(−3, −55).