Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.
Identify the vertex from completed-square form of a quadratic
Problem
Use completed-square form \(f(x)=2(x-3)^2+5\) to identify the vertex.
Big Picture
What this problem is really about
Completed-square form makes the vertex a parameter-reading problem. We’ll match the rule to a times the square of x minus h, plus k, reverse the sign inside the binomial, and verify the coordinates where the squared term becomes zero.
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