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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

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

(−6,206)

1 answer

To determine which point can be generated to create the parabola for the quadratic equation \( y = -6x^2 + 3x + 8 \), we can evaluate the equation at the given x-values and see if we get the corresponding y-values.

Let's check each option one by one.

  1. For the point \((-3, 323)\): \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \] This point does not satisfy the equation.

  2. For the point \((-3, -55)\): We have already calculated this when checking \((-3, 323)\), and we found: \[ y = -55 \] This point satisfies the equation.

  3. For the point \((-6, 8)\): \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \] This point does not satisfy the equation.

  4. For the point \((-6, 206)\): Using the same calculations as above: \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \] Again, this point does not satisfy the equation.

Thus, the only point that satisfies \( y = -6x^2 + 3x + 8 \) is:

\((-3, -55)\)