Complete the square to transform quadratics and derive the quadratic formula.
Rewrite a quadratic in standard form as vertex form by completing the square
Problem
Rewrite \(f(x)=x^{2}+10x+18\) in vertex form by completing the square. State the half-coefficient and square added, preserve equivalence, identify the vertex, and confirm by expansion.
Big Picture
What this problem is really about
Vertex form comes from turning the quadratic and linear terms into one perfect square. We’ll halve the linear coefficient and square it, add and subtract that value to preserve equivalence, factor the trinomial, and then read the vertex by reversing the sign inside the squared binomial.
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