Write the function in vertex form.

Question

y=x^2 + 6x + 1

Answer 1

y = a (x-h)²+k

y= x²+ 6x + 1 (Ignore y and replace with 0)

0 = x²+ 6x + 1 (subtract 1 on both side)

-1 = x²+ 6x (take b/2 and square on both side)

-1 + (6/2)² = x²+ 6x + (6/2)²

-1 + (3)² = x²+ 6x + (3)²

-1+9 = x²+ 6x + 9

8 = x²+ 6x + 9 (rewrite as factor form)

8 = (x+3)(x+3)

8 = (x+3)² (subract 8 over and bring your y back)

y= (x+3)² - 8 (This is a vertex form)