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

Question

A. -9/5

B. 9

C. 5/18

D. -5/9

Answer 1

The standard form of the equation of a parabola is

 

f(x)  = a x² + b x + c.

 

With this standard from, the x coordinate of the vertex  is   -b/(2a).

 

Comparing with the function given, we see that

a = -9     b =  5 and  c = 9

 

So  the x coordinate of the vertex is     - 5 /(2 (-9)) =  5/18.

 

Algebra 2 students should memorize  the -b /( 2 a)  rule - it is too hard to work out by completing the square.

 

Calculus students can easily derive it by setting the derivative of f(x) equal to zero in order to identify the critical point that is the vertex.   This leads to:   2 a x + b = 0 ,  which implies   x =  - b/( 2 a)