Complete the square to reveal maximum or minimum values of quadratic functions.
Complete the square for a nonmonic quadratic
Problem
Rewrite \(2x^{2}+12x+5\) in vertex form. Factor \(2\) from only the variable terms, complete the square inside the parentheses, distribute the compensation correctly, and identify the vertex.
Big Picture
What this problem is really about
For a nonmonic quadratic, completing the square starts by factoring the leading coefficient from only the variable terms. We’ll complete the square inside that group, remember that the outside coefficient scales the compensation too, combine the constants, and expand after reading the vertex to verify equivalence.
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