The parabola shown above has its minimum point at (0.5, -16). What is its equation?

f(x)= -4x^{2} - 4x - 15

f(x)= -4x^{2} + 4x - 15

f(x)= 4x^{2} - 4x - 15

f(x)= 4x^{2} + 4x - 15

Thank you for the opportunity to help you with your question!

Answer C

A minimum point occurs when the coefficient of x² (the number in front of x² is positive

so the answer is either C or D.

The easiest way to check is to get the answer is to check if (0.5, -16) lies on C or D

It lies on C because 4 (0.5)² - 4 (0.5) -15 = 1 - 2 -15 = -16 so (0.5, -16) lies on this parabola.

You can also get the answer by completing the square (2x -1)² -16

or by differentiating.

Let me know if you want me to do this too.

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