Which of the following is a point you can generate to create the parabola for the quadratic equation y=−6x^2+3x+8

Question

?(1 point)
Responses

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

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

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

(−6,206)

Answer 1

To determine which of the given points lies on the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute each x-value from the points into the equation and see if we get the corresponding y-value.

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

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

3. Point \((-3, -55)\): \[ y = -6(-3)^2 + 3(-3) + 8 \ = -6(9) - 9 + 8 \ = -54 - 9 + 8 \ = -55 \quad (\text{This point works!}) \]

4. Point \((-6, 206)\): \[ y = -6(-6)^2 + 3(-6) + 8 \ = -6(36) - 18 + 8 \ = -216 - 18 + 8 \ = -226 \quad (\text{Not } 206) \]

The only point that satisfies the equation is \((-3, -55)\).

Therefore, the correct answer is: (−3,−55).