Chapter 5 Polynomials and Polynomial Functions - 5.8 Analyze Graphs of Polynomial Functions - 5.8 Exercises - Mixed Review - Page 392: 52

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The vertex form of a quadratic function: $y=a(x-h)^2+k$ The vertex is $(-4,-6)$, so we know $h=-4\\k=-6$ The function becomes: $y=a(x-(-4))^2+(-6)\\y=a(x+4)^2-6$ We notice that $(2,3)$ is on the graph, so we will substitute: $3=a(2+4)^2-6\\\rightarrow 36a-6=3\\ \rightarrow 36a=9\\\rightarrow a=\frac{1}{4}$ Hence, $y=\frac{1}{4}(x+4)^2-6$