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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)
left parenthesis negative 6 comma 206 right parentheis

1 answer

To determine which point lies on the parabola represented by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the x-coordinates from the provided options into the equation and see if the corresponding y-value matches.

Let's evaluate each point:

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

  2. For (-3, -55): \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \] This matches, so (-3, -55) is indeed a point on the parabola.

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

  4. For (-6, 206): \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \] This does not match 206.

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