Question

F(x)=x2−8x+3 in vertex form

Answer 1

f(x)=(x+4)2−13

Converting to Vertex Form
1. Start by placing brackets around the first two terms.

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

2. In order to make the bracketed terms a perfect square trinomial, we must add a "c" term as in ax2+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 ax2+bx+c to bring it outside the brackets.

f(x)=(1x2+8x+(82)2)+3−((82)2×1)

5. Simplify.

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

6. Lastly, factor the perfect square trinomial.

f(x)=(x+4)2(squared)−13