Given the equation of a quadratic function:
![f(x)=(x-1)^2+3](https://img.qammunity.org/2023/formulas/mathematics/college/t035m7mzzfky15z3751k3emidh3g0e4ujk.png)
Form the given equation, the vertex will be (1, 3)
We will graph the function using three points
The vertex and two pairs of symmetric points
so, substitute with x = {-1, 3}
![\begin{gathered} f(-1)=(-1-1)^2+3=(-2)^2+3=4+3=7 \\ f(3)=(3-1)^2+3=(2)^2+3=4+3=7 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/o6kt24kgziwb7hlas0x09f2xgzp3xt3hs7.png)
so, the points are: (-1, 7), (1, 3), and (3, 7)
the graph of the function will be as shown in the following picture: