Given the quadratic equation:

To create a sketch of the quadratic function, follow the steps below.
Step 01: Find the x-intercepts.
The x-intercepts are the zeros of the function and can be found using the quadratic formula:
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://img.qammunity.org/2023/formulas/mathematics/college/rxvf73usjbbwyik14knxdemoz21vfz2ufc.png)
In this question:
a = 1
b = -7
c = 3
Then,
![\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot1\cdot3}}{2\cdot1} \\ x=\frac{7\pm\sqrt[]{49-12}}{2}=\frac{7\pm\sqrt[]{37}}{2} \\ x_1=\frac{7-\sqrt[]{37}}{2}=0.5 \\ x_2=\frac{7+\sqrt[]{37}}{2}=6.5 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/rz6miwxmhuydqwg8rnve8v4hid6d7flc6o.png)
So, the equation has the points (0.5, 0) and (6.5, 0).
Step 02: Find the vertex.
The x-vertex is:

And, the y-vertex is:

So, the vertex is the point (3.5, -9.25).
Step 03: Find the axis of symmetry.
The axis of symmetry is the line x = xv.
So, the axis of the symmetry is x = 3.5.
Step 04: Draw the graph.
Plot the point and connect them. Then, draw the axis of symmetry.