Complete the square to transform quadratics and derive the quadratic formula.
Identify the maximum or minimum of a quadratic written in vertex form
Problem
For \(f(x)=(x-3)^{2}+2\), identify coefficient sign, opening direction, vertex, maximum/minimum type, extremum value, \(x\)-location, and range.
Big Picture
What this problem is really about
Vertex form separates the parabola’s turning point from the coefficient that controls its opening. We’ll read h by reversing the sign inside the parentheses, use k as the vertex’s output, and use the positive or negative leading coefficient to decide whether that output is a minimum or maximum and which way the range extends.
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