Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.
Identify the zeros of a quadratic from factored form
Problem
Use factored form \(f(x)=(x-2)(x+5)\) to identify zeros.
Big Picture
What this problem is really about
Factored form exposes zeros through the zero-product property. We’ll set the product equal to zero, solve each factor equation separately with careful sign handling, and substitute both inputs to confirm that each makes the function vanish.
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