Question

Write each quadratic function in the form f(x)=a(x−h)2+k, find the vertex
1. y=x^2-3x
2. y=x^2+x
3. y=2x^2−12x+22
4. y=−2x^2−4x−5

Answer 1

I will do one, you follow the same steps with the others.

3. y=2x^2−12x+22

step1: factor out the coefficient of the square term from the first two terms if it is other than +1,
I let the constant tag along at the end
y = 2(x^2 - 6x ) + 22

step2. take 1/2 of the coefficient of the x term inside the bracket, square it, then add it then subtract it within the bracket.
y = 2(x^2 - 6x <b>+ 9 - 9</b>) + 22
step3. write the first 3 terms inside the bracket as a perfect square
y = 2( <b>(x-3)^2</b> - 9) + 22

step4. distribute the outside factor over the two terms inside the bracket
y = 2(x-3)^2 - 18 + 22

step 5. simplify the constants at the end, and you are done!

y = 2(x-3)^2 + 4

so the vertex is (3,4)