Question

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

A. (-6,8)
B. (-3,323)
C. (-3,-55)
D. (-6,206)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To generate points to create the parabola for the quadratic equation y = -6x^2 + 3x + 8, we can substitute different values of x into the equation and solve for y.

Let's plug in x = -6:
y = -6(-6)^2 + 3(-6) + 8
y = -6(36) - 18 + 8
y = -216 - 18 + 8
y = -226 + 8
y = -218

So, when x = -6, y = -218.

Therefore, the point (-6, -218) is generated by the quadratic equation y = -6x^2 + 3x + 8.

None of the given options match this point, so none of the options are correct.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the points that you can use to generate the parabola for the quadratic equation y = -6x^2 + 3x + 8, you can substitute different x-values into the equation and solve for y.

Let's substitute the x-values from the answer choices and see which points satisfy the equation:

A. (-6,8):
Substituting x = -6 into the equation:
y = -6(-6)^2 + 3(-6) + 8
= -6(36) - 18 + 8
= -216 - 18 + 8
= -226 + 8
= -218

B. (-3,323):
Substituting x = -3 into the equation:
y = -6(-3)^2 + 3(-3) + 8
= -6(9) - 9 + 8
= -54 - 9 + 8
= -55

C. (-3,-55):
Substituting x = -3 into the equation:
y = -6(-3)^2 + 3(-3) + 8
= -6(9) - 9 + 8
= -54 - 9 + 8
= -55

D. (-6,206):
Substituting x = -6 into the equation:
y = -6(-6)^2 + 3(-6) + 8
= -6(36) - 18 + 8
= -216 - 18 + 8
= -226 + 8
= -218

Based on the calculations, the points that satisfy the equation and can be used to generate the parabola are:

A. (-6,8)
C. (-3,-55)

Answer 3

[AI-generated answer — Explain Bot]

To generate points on the parabola for the quadratic equation y = -6x^2 + 3x + 8, you need to substitute different values of x into the equation to find the corresponding y-values. Let's substitute the x-values from the given options one by one and see which point satisfies the equation.

A. (-6,8):
Substituting x = -6 into the equation:
y = -6(-6)^2 + 3(-6) + 8
y = -6(36) - 18 + 8
y = -216 - 18 + 8
y = -226
So, the point (-6, 8) does not satisfy the equation.

B. (-3,323):
Substituting x = -3 into the equation:
y = -6(-3)^2 + 3(-3) + 8
y = -6(9) - 9 + 8
y = -54 - 9 + 8
y = -55
So, the point (-3, 323) does not satisfy the equation.

C. (-3,-55):
Substituting x = -3 into the equation:
y = -6(-3)^2 + 3(-3) + 8
y = -6(9) - 9 + 8
y = -54 - 9 + 8
y = -55
So, the point (-3, -55) satisfies the equation.

D. (-6,206):
Substituting x = -6 into the equation:
y = -6(-6)^2 + 3(-6) + 8
y = -6(36) - 18 + 8
y = -216 - 18 + 8
y = -226
So, the point (-6, 206) does not satisfy the equation.

Therefore, the correct point that can generate the parabola for the quadratic equation is C. (-3, -55).