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

Question

?(1 point)
Responses

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

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

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

(−3,323)

Answer 1

To determine which of the provided points lies on the parabola described by the equation \( y = -6x^2 + 3x + 8 \), we can substitute the x-coordinates of each point into the equation and see if we get the corresponding y-coordinate.

Let's evaluate each option:

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

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

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

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

The point that lies on the parabola given by the quadratic equation \( y = -6x^2 + 3x + 8 \) is (-3, -55).