Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Build a quadratic function from two zeros and one point
Problem
Using the plotted zeros \(2\) and \(6\), start with \(f(x)=a(x-2)(x-6)\). Substitute the point \((0,12)\), solve for \(a\), and check both zeros and the extra point in the completed function.
Two zeros determine the linear factors of the quadratic, while one more point determines their shared scale. We’ll build the factored template, substitute the extra point with both factor signs intact, solve for the scale, and verify the final function at all three supplied graph features.
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