Question

Rewrite the quadratic expression in vertex form by completing the square. You must show all work.

Answer 1

Answer:

$f(x)=(x-1)^{2}+6$

Step-by-step explanation:

First, subtract 7 from each side.

$-7=x^{2} -2x$

Now, add in a blank on each side so you can write in your new term that will complete the square. We'll call that term 's' for now.

$-7+s=x^{2} -2x+ s$

The next step is to take half of the b term, and then square that. In this case, half of '$-2$' is $-1$. If we square that we get $1$. So that is the term we will put in for $s$.

$-7+1=x^{2} -2x+1$

Simplify:

$-6=x^{2} -2x+1$

If you look at the right side of the equation, we can factor. That's because we completed the square. We can use the 'guess and check' method to factor. Remember, this is where we use 2 sets of parentheses and fill in the blanks.

$-6=(x-1)(x-1)$

If we were to FOIL the right side we would end up with $x^{2} -2x+1$.  

Since we have 2 '(x-1)' terms next to each other, we can simplify to:

$-6=(x-1)^{2}$

Now, all we need to do is add 6 to both sides and we have the vertex form.

$f(x)=(x-1)^{2}+6$

I hope this helps!