SOLUTION: Change the following to vertex form: 1. f(x)=x²-12x+16 2. f(x)=x²+4x+1

Algebra ->  Rational-functions -> SOLUTION: Change the following to vertex form: 1. f(x)=x²-12x+16 2. f(x)=x²+4x+1       Log On


   

Question 1008751: Change the following to vertex form:
1. f(x)=x²-12x+16
2. f(x)=x²+4x+1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex form of a quadratic is given by
+f%28x%29=+a%28x+-+h%29%5E2+%2B+k, where (h, k) is the vertex.
The "a" in the vertex form is the same "a" as in +f%28x%29+=+ax%5E2+%2B+bx+%2B+c (that is, both a's have exactly the same value).
1.
f%28x%29=x%5E2-12x%2B16......complete square
f%28x%29=%28x%5E2-12x%2Bb%5E2%29-b%5E2%2B16
f%28x%29=%28x%5E2-12x%2B6%5E2%29-6%5E2%2B16
f%28x%29=%28x-6%29%5E2-36%2B16
f%28x%29=%28x-6%29%5E2-20
the vertex is at (6, -20)

2.
f%28x%29=x%5E2%2B4x%2B1+
f%28x%29=%28x%5E2%2B4x%2Bb%5E2%29-b%5E2%2B1+
f%28x%29=%28x%5E2%2B4x%2B2%5E2%29-2%5E2%2B1+
f%28x%29=%28x%2B2%29%5E2-4%2B1+
f%28x%29=%28x%2B2%29%5E2-3+
the vertex is at (-2, -3)