Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.
Complete the square and identify the extremum
Problem
Complete the square for \(x^{2}-6x+2\) by adding and subtracting \(9\). Write the equivalent vertex form, expand it as a check, and use the leading coefficient to state the vertex and whether it is a maximum or minimum.
Big Picture
What this problem is really about
Completing the square trades standard form for a form that displays symmetry and the extremum. We’ll square half the linear coefficient, add and subtract that same amount to preserve equivalence, form the perfect square, and interpret the remaining parameters.
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