Solve simple linear-quadratic systems algebraically and graphically.
Solve a linear-quadratic system by substituting the line equation into the quadratic
Problem
Solve \(y=(x-2)^{2}+1\) and \(y=5\) by substitution. Isolate the squared expression, use both root branches, form the ordered pairs, and check them against the displayed answer graph.
Big Picture
What this problem is really about
At an intersection, the vertex-form quadratic and horizontal line must produce the same output. We’ll set those outputs equal, isolate the entire squared expression before taking roots, keep both branches, and use the line’s fixed height to form and check both graph points.
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