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

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

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

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

(−6,8)

Answer 1

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

1. For \( x = -3 \):
\[
y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55
\]
Thus, the point \( (-3, -55) \) is on the parabola.

2. For \( x = -6 \):
\[
y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226
\]
The point \( (-6, 206) \) is not on the parabola since \( y \) should be -226, not 206.

3. For \( x = -6 \) again (to check the point \( (-6, 8) \)):
As calculated above, it is not valid, since we found \( y = -226 \) when \( x = -6 \).

4. For \( x = -3 \) again (it was already checked):
The valid point is \( (-3, -55) \).

Thus, from your options, the correct point that generates a position on the parabola defined by the equation is:

\[
(-3, -55)
\]