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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=−6x2+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=−6x2+3x+8 is:

(−3,−55)