Graph linear and quadratic functions and identify intercepts, maxima, and minima.
List graphing features of a quadratic in vertex form
Problem
List the graphing features of \(y=(x-2)^{2}+3\). Identify \(a\), \(h\), and \(k\), vertex, symmetry axis, opening, and width, then calculate the outputs at \(x=1\) and \(x=3\) to produce and verify a symmetric point pair.
Big Picture
What this problem is really about
Vertex form separates a parabola’s center from its shape. We’ll read the vertex and symmetry axis from the shifts, use the leading coefficient for opening and width, and test two equally spaced inputs to build a symmetric point pair.
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