Complete the square to write the function in vertex form

Question

Complete the square to write the function in vertex form.

f(x)=2x+12x+13

Answer 1

I am assuming that you mean f(x) = 2x² + 12x + 13.

 

The "vertex form" of a quadratic function is f(x) = a(x - h)² + k. The graph of f is a parabola with vertex (h, k).  If a > 0, then (h, K) is the lowest point of the graph and if a < 0, then (h, k) is the highest point of the graph.   

 

f(x) = 2(x² + 6x) + 13      

 

To complete the square, take half of the coefficient of x and square that number.  So, in this particular example, we have

[(1/2)(6)]² = 9.  Then add and subtract 9 inside the parentheses.

 

f(x) = 2(x² + 6x + 9 - 9) + 13

 

f(x) = 2(x + 3)² - 18 + 13

 

f(x) = 2(x + 3)² - 5

 

f(x) = 2(x - (-3))² + (-5).  So, h = -3 and k = -5.

 

(h, k) = (-3, -5) is the lowest point on the graph.