Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Build a quadratic function in vertex form from a vertex and one point
Problem
Using the graph’s vertex \((2,5)\) and point \((4,13)\), begin with \(f(x)=a(x-2)^{2}+5\). Substitute the point, solve for \(a\), write the completed function, and check both givens.
A known vertex fixes h and k in vertex form, leaving only the vertical scale unknown. We’ll substitute the second graph point, square its full horizontal displacement before solving for the scale, and check the completed function against both the vertex and the additional point.
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