Identify zeros from factorizations and use them to sketch polynomial graphs.
Find the y-intercept of a polynomial written in factored form
Problem
Find the \(y\)-intercept of \(p(x)~=~(x~-~2)(x~+~3)\).
Big Picture
What this problem is really about
An intercept on the y-axis occurs where the input is zero, so this is an evaluation problem rather than a zero-finding problem. Substitute zero into the factored expression without expanding first, compute the output, and write the result as an ordered pair whose first coordinate is zero.
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