Chapter 4 Quadratic Functions and Factoring - 4.1 Quadratic Functions in Standard Form - 4.1 Exercises - Skill Practice - Page 241: 54

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The x-coordinate of the vertex is $x=\frac{-b}{2a}$ Substitute this into the given equation: $$y=a(\frac{-b}{2a})^2+b(\frac{-b}{2a})+c\\ \rightarrow y=a(\frac{b^2}{4a^2})-\frac{b^2}{2a}+c\\ \rightarrow y=\frac{ab^2}{4a^2}-\frac{b^2}{2a}+c\\ \rightarrow y=\frac{ab^2-(2a)b^2}{4a^2}\\ \rightarrow y=\frac{ab^2-2ab^2}{4a^2}+c\\ \rightarrow y=\frac{-ab^2}{4a^2}+c\\ \rightarrow y=\frac{-b^2}{4a}+c$$