SOLUTION: Please write the quadratic function in the form {{{f(x)=a(x-h)^2+k}}} by the COMPLETING THE SQUARE METHOD. Please then identify the vertex. {{{h(x)=x^2+4x+5}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please write the quadratic function in the form {{{f(x)=a(x-h)^2+k}}} by the COMPLETING THE SQUARE METHOD. Please then identify the vertex. {{{h(x)=x^2+4x+5}}}      Log On


   

Question 331594: Please write the quadratic function in the form f%28x%29=a%28x-h%29%5E2%2Bk by the COMPLETING THE SQUARE METHOD. Please then identify the vertex.
h%28x%29=x%5E2%2B4x%2B5
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
To complete the square, you need to halve the b term (b=4 in your question) and then square it. Half of b=4 is 2. Square it and you will get 4 again. Now add 4:

x^2 + 4x + 4 + 5 - 4

Notice that I also subtracted 4 at the end. This is because you are not just allowed to add 4 to the equation, you can only add zero. You achieve this by subtracting the same number afterwards. Now x^2+4x +4 can be turned into a perfect square:

=(x^2 + 4x + 4) + 5 - 4
=(x+2)^2 +1

Now it is in the form you want. The vertex is (-2,1).