F (x) = x2-8x+3 in vertex form

f (x) = (x+4) 2 - 13

Converting to Vertex Form

1. Start by placing brackets around the first two terms.

f (x) = x2 + 8x+3 f (x) = (x2 + 8x) + 3

2. In order to make the bracketed terms a perfect square trinomial, we must add a "c" term as in a x2 + bx+c. Since c, in a perfect square trinomial is denoted by the formula c = (b2) 2, take the value of b to find the value of c.

f (x) = (x2 + 8x + (82) 2) + 3

3. However, adding (82) 2 would change the value of the equation. Thus, subtract (82) 2 from the (82) 2 you just added.

f (x) = (x2 + 8x + (82) 2 - (82) 2) + 3

4. Multiply ( - (82) 2) by the a term as in a x2 + bx+c to bring it outside the brackets.

f (x) = (1 x2 + 8x + (82) 2) + 3 - ((82) 2 * 1)

5. Simplify.

f (x) = (x2 + 8x+16) + 3-16 f (x) = (x2 + 8x+16) - 13

6. Lastly, factor the perfect square trinomial.

f (x) = (x+4) 2 (squared) - 13