select the x-coordinate

Question

Select the x-coordinate of the vertex of the parabola defined by the function f(x) = -3x2 + 5x + 9.

A. -3/5

B. 9

C. 5/6

 

D. -5/3

Answer 1

In the form f(x) = a(x - h)² +k, h is x-coordinate of the vertex. Use completion of the square to alter the form of the given function.

 

f(x) = -3x² + 5x + 9

f(x) = -3(x² - 5x/3        ) + 9

f(x) = -3(x² - 5x/3 + (5/6)²) + 9 + 3(5/6)²

f(x) = -3(x - 5/6)² + 133/12

 

The x-coordinate of the vertex is 5/6, C.