Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.
Find the vertex of a quadratic from factored form
Problem
Use factored form \(f(x)=(x-1)(x-5)\) to find the vertex.
Big Picture
What this problem is really about
Factored form locates a quadratic’s vertex through symmetry without requiring expansion. We’ll read the roots, average them for the axis input, evaluate the original product there, and use the leading coefficient’s sign to classify the extremum.
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