Chapter 5 Polynomials and Polynomial Functions - 5.8 Analyze Graphs of Polynomial Functions - 5.8 Exercises - Mixed Review - Page 392: 51

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The vertex form of a quadratic function: $y=a(x-h)^2+k$ The vertex is $(5,4)$, so we know $h=5\\k=4$ The function becomes: $y=a(x-5)^2+4$ We notice that $(3,12)$ is on the graph, so we will substitute: $12=3(x-5)^2+4\\\rightarrow 4a+4=12\\ \rightarrow 4a=8\\\rightarrow a=2$ Hence, $y=2(x-5)^2+4$