Question

Complete the square and find the vertex form of the quadratic function.
f(x)= x^2 -2x+5

Answers

Answered by GPT 3.5
To complete the square, we need to take the coefficient of the x term, divide it by 2, and then square the result. For the quadratic function f(x) = x^2 - 2x + 5:

1. Take half of the coefficient of the x term: -2/2 = -1
2. Square the result: (-1)^2 = 1

Now let's rewrite the quadratic function by adding and subtracting 1 inside the parentheses:

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

Next, let's group the square term with the constant term:

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

The grouped terms x^2 - 2x + 1 can be written as a square of a binomial:

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

Simplifying further:

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

Therefore, the vertex form of the quadratic function is f(x) = (x - 1)^2 + 4. The vertex of the parabola is (1, 4).
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