Write in vertex form

Question

write f(x)=x^2+10x+15 in vertex form

Answer 1

We have to complete the square. First, move the 15 to the other side by subtracting it out.

 

x² + 10x = -15

 

Now, take half of 10, square it, and add it to both sides.

 

x² + 10x + 25 = -15 + 25

 

Now take that half of 10, throw it with the x in parentheses, and square the whole shebang (because x² + 10x + 25 = (x + 5)²)

 

(x + 5)² = 10

f(x) = (x + 5) - 10