E-CS04 · Two quadratics with the same minimum
For a real parameter \(h\), let \(g_h(x)=x^2-2hx+h+4\).
Find the minimum value of \(g_h\) in terms of \(h\), and state where it occurs.
Find all \(h\) for which this minimum equals 2.
For each value of \(h\) from part (b), solve \(g_h(x)=6\).
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