To graph the quadratic equation, we can use a table of values.
Step 1: We make a two-column table. We label the columns x and y.
Step 2: We choose several values for x and put them as separate rows in the x column.
Step 3: We evaluate the function for each value of x.
[tex]\begin{gathered} x=-3 \\ y=x^2-\frac{3}{4}x+\frac{1}{8} \\ y=(-3)^2-\frac{3}{4}(-3)+\frac{1}{8} \\ y=9+\frac{9}{4}+\frac{1}{8} \\ y=\frac{72}{8}+\frac{18}{8}+\frac{1}{8} \\ y=\frac{91}{8} \\ y=11.375 \end{gathered}[/tex]
[tex]\begin{gathered} x=-2 \\ y=x^2-\frac{3}{4}x+\frac{1}{8} \\ y=(-2)^2-\frac{3}{4}(-2)+\frac{1}{8} \\ y=4+\frac{6}{4}+\frac{1}{8} \\ y=\frac{32}{8}+\frac{12}{8}+\frac{1}{8} \\ y=\frac{32+12+1}{8} \\ y=5.625 \end{gathered}[/tex]
And so on.
Step 4: We write the result in the y column next to the x value we used.
Step 5: We plot and join the found ordered pairs.
Therefore, the graph of the quadratic equation is:
