Let's start by recalling the of a .
Vertex Formf(x)=a(x−h)2+k
In this format, the is located at (h,k).
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Since we want our function to have a vertex at (1,3) we can wirte it in vertex form using h=1 and k=3. Note that a can take any value as it does not affect the location of the vertex. For simplicity, we will use a=1.
f(x)=1(x−1)2+3⇔f(x)=(x−1)2+3
Notice that we could have chosen any nonzero value for a. Therefore, there are infinitely many quadratic functions whose vertex is located at (1,3). This is just one example.