Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Rewrite a quadratic to reveal its vertex
Problem
Rewrite \(f(x)=x^{2}-6x+2\) in vertex form by completing the square. Track the half-coefficient and compensation, identify the vertex, expand to verify, and compare with the displayed answer graph.
Big Picture
What this problem is really about
Completing the square rewrites the quadratic without changing its values. We’ll halve the linear coefficient, add and subtract its square as a balanced compensation, combine the perfect-square trinomial and remaining constants, and use vertex form to read the turning point before expanding to verify the rewrite.
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