Chapter 4 Quadratic Functions and Factoring - 4.2 Graph Quadratic Functions in Vertex or Intercept Form - 4.2 Exercises - Skill Practice - Page 250: 49

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This function is in the form $a(x-p)(x-q)$. We know that the axis of symmetry is $\frac{p+q}{2}$. We need the axis of symmetry to be $x=3$. Then, $\frac{p+q}{2}=3\\\rightarrow p+q=6\\ \rightarrow p=6-q$ Assume $q=2 \rightarrow p=6-2=4$ Obtain the function: $y=(x-4)(x-2)$ $q=4 \rightarrow p=6-4=2$ Obtain the function: $y=(x-2)(x-4)$