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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

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

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

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

(−6,206)

1 answer

To determine which point can be generated to create the parabola described by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the x-coordinates from each of the given points into the equation and see if the corresponding y-coordinate matches the output of the equation.

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

  2. For \( (-3, -55) \): \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \] Result: \( (-3, -55) \) satisfies the equation.

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

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

The only point that satisfies the quadratic equation \( y = -6x^2 + 3x + 8 \) is \( (-3, -55) \).