SOLUTION: Review question for test: I cannot find out how they got this answer Rewrite the function in the form y=a(x-h)squared: y=xsquared +4x+1 Answer is y=(x+2)squared-3 How di

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Review question for test: I cannot find out how they got this answer Rewrite the function in the form y=a(x-h)squared: y=xsquared +4x+1 Answer is y=(x+2)squared-3 How di      Log On


   

Question 172339This question is from textbook
: Review question for test: I cannot find out how they got this answer
Rewrite the function in the form y=a(x-h)squared: y=xsquared +4x+1
Answer is y=(x+2)squared-3
How did they get this answer, I would like to see the work showed
 This question is from textbook

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
They arrived to that ANSWER by Completing the Square:
Here it goes:
Given --------->y=x%5E2%2B4x%2B1
y=%28x%5E2%2B4x%2B4%29highlight%28-4%29%2B1, Remember to add "+4" to make it a perfect square, and DON'T FORGET to subtract "-4" so it won't change the expression.
Why 4? Take "half" of the middle term constant (which is 4 = 4/2=2), then squared it ---> 2%5E2=highlight%284%29
.
Continuing, highlight%28y=%28x%2B2%29%5E2-3%29 Answer----> vertex form=a%28x-h%29%5E2%2Bk; h=-2,k=-3>>> Vertex (-2,-3), As you see on the graph:

Thank you,
Jojo