Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.
Choose the equivalent quadratic form that best reveals zeros
Problem
Rewrite \(x^{2}-7x+10\) in the form that exposes its zeros directly. Find \(\text{two}~\text{numbers}\) with product \(10\) and sum \(-7\), verify the expansion, and state the zeros visible from the factors.
Big Picture
What this problem is really about
Equivalent quadratic forms are useful because each exposes a different feature. We’ll match the requested zeros to a product of linear factors, build that product from a signed pair with the required sum and product, and expand to confirm equivalence.
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