x coordinate of vertex

Question

f(x)=-5x^2+9x+6

Answer 1

y = -5x² + 9x + 6

 

There are two ways to do this algebraically.  The easiest way is to remember that the x-coordinate of the vertex is ALWAYS located at:

 

x = -b/2a

 

where a is the coefficient of the x² term and b is the coefficient of the x term.  In this case, a = -5 and b = 9, so the x-coordinate of the vertex is:

 

x = -9/2*(-5) = 9/10

 

The second method is to "complete the square" on the original equation and put it into the vertex form, y = (x-h)² + k where (h,k) is the location of the vertex:

 

y = -5(x² - (9/5)x + (-9/10)²) + 6 - 5*(-9/10)²

 

y = -5(x - 9/10)² + 1.95

 

The vertex is located at (9/10,1.95).  Click on the link below for a short tutorial on how to "complete the square":

 

http://www.mathsisfun.com/algebra/completing-square.html