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

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

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

(−3,323)

Answer 1

To find a point that lies on the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the values of \( x \) from each of the provided point options into the equation and see if we get the corresponding \( y \) value.

Let's calculate \( y \) for each of the given points:

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

2. For the point \( (-6, 8) \):
\[
y = -6(-6)^2 + 3(-6) + 8
\]
The calculation is the same as above and results in \( y = -226 \quad \text{(not 8)} \).

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

4. For the point \( (-3, 323) \):
\[
y = -6(-3)^2 + 3(-3) + 8
\]
The calculation is the same as above and results in \( y = -55 \quad \text{(not 323)} \).

The only point that lies on the parabola given by the quadratic equation \( y = -6x^2 + 3x + 8 \) is:

**Answer: \((-3, -55)\)**