Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.
Find a missing parameter in a quadratic from its structured form and a given feature
Problem
Find the missing parameter \(a\) in \(f(x)=a(x-2)(x-6)\) if the \(y\text{-}\text{intercept}\) is \(12\).
Big Picture
What this problem is really about
A stated graph feature becomes an equation for the missing parameter. We’ll translate the named intercept into its fixed input-output condition, substitute that point into the structured quadratic, solve the resulting one-variable equation, and check the original feature.
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