Question

1. Which of the following is a point you can generate to create the parabola for the quadratic equation y = -6x² + 3x + 8?
• (-3,-55)
• (-6,206)
• (-3,323)
• (-6,8)

Answer 1

To determine which of the following points can be used to generate the parabola for the quadratic equation, we need to substitute the x-coordinate of each point into the equation and check if it matches the y-coordinate.

Let's substitute the x-coordinate of each point into the quadratic equation:

1. (-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

The y-coordinate matches (-3,-55), so this point can be used to generate the parabola.

2. (-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 + 8
y = -218

The y-coordinate does not match (-6,206), so this point cannot be used to generate the parabola.

3. (-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

The y-coordinate does not match (-3,323), so this point cannot be used to generate the parabola.

4. (-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 + 8
y = -218

The y-coordinate does not match (-6,8), so this point cannot be used to generate the parabola.

Therefore, the only point that can be used to create the parabola for the quadratic equation y = -6x² + 3x + 8 is (-3,-55).