Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.
Identify the maximum or minimum of a quadratic
Problem
From this quadratic graph or rule, identify any maximum or minimum: \(y=(x-3)^2+2\).
Big Picture
What this problem is really about
The vertex tells both where an extremum occurs and what its extreme output is, but those are different coordinates. We’ll read the vertex from vertex form, use the leading coefficient to classify it as a maximum or minimum, and confirm the output bound from the nonnegative squared term. That keeps the input location from being confused with the extremum value.
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