Problem

Find the vertex of the function f(x)=2x2−4x+1.

Answer

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Answer

Step 6: So, the vertex (h,k) of the function is (1,−1).

Steps

Step 1 ：Step 1: The vertex form of a parabola is f(x)=a(x−h)2+k, where (h,k) is the vertex of the parabola. Let's convert the given function into the vertex form.

Step 2 ：Step 2: The function f(x)=2x2−4x+1 can be rewritten as f(x)=2(x2−2x)+1.

Step 3 ：Step 3: Adding and subtracting 1 inside the parenthesis, we get f(x)=2[(x2−2x+1)−1]+1.

Step 4 ：Step 4: Now, f(x)=2[(x−1)2−1]+1.

Step 5 ：Step 5: Simplifying further, f(x)=2(x−1)2−2+1, which is f(x)=2(x−1)2−1.

Step 6 ：Step 6: So, the vertex (h,k) of the function is (1,−1).

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