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

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

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

(−6,8)

Answer 1

To determine which of the given points is on the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the x-coordinates of each point into the equation and see if the resulting y-value matches the y-coordinate of the point.

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

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

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

\[
\boxed{(-3, -55)}
\]