Graph linear and quadratic functions and identify intercepts, maxima, and minima.
Identify the maximum or minimum of a quadratic from its equation
Problem
Use the vertex form \(y=(x-2)^{2}-5\) to identify the vertex. Apply the bound \((x-2)^{2}\ge~0\) and the sign of its coefficient to determine the opening direction, the extremum and where it occurs, and the range. Identify the feature statement justified by all of these results.
Big Picture
What this problem is really about
In vertex form, the squared expression provides a built-in bound on every output. We’ll locate the vertex, use the coefficient’s sign to decide whether that bound is a minimum or maximum, identify where equality occurs, and translate the result into a range.
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