In order to determine the value of p(3/4), we just have to replace 3/4 for x, like this:
[tex]\begin{gathered} p(\frac{3}{4})=2(\frac{3}{4})^2+9\frac{3}{4}-9 \\ \end{gathered}[/tex]
Then, we just have to simplify this expression to determine the vapue of p(3/4), like this:
[tex]\begin{gathered} p(\frac{3}{4})=2\frac{3^2}{4^2}^{}+9\frac{3}{4}-9 \\ p(\frac{3}{4})=2\frac{9}{16}^{}+9\frac{3}{4}-9 \\ p(\frac{3}{4})=\frac{2\times9}{16}+\frac{9\times3}{4}-9 \\ p(\frac{3}{4})=\frac{18}{16}+\frac{27}{4}-9 \\ p(\frac{3}{4})=\frac{9}{8}+\frac{27}{4}-9 \end{gathered}[/tex]
By multiplying the denominator and numerator of the second fraction by 2 we can make the the denominator 8 and add the two fractions:
[tex]\begin{gathered} p(\frac{3}{4})=\frac{9}{8}+\frac{27\times2}{4\times2}-9 \\ p(\frac{3}{4})=\frac{9}{8}+\frac{54}{8}-9 \\ p(\frac{3}{4})=\frac{9+54}{8}-9 \\ p(\frac{3}{4})=\frac{63}{8}-9 \end{gathered}[/tex]
Similarly, by multipling by 8 and dividing by 8 the last term, -9, we get:
[tex]\begin{gathered} p(\frac{3}{4})=\frac{63}{8}-\frac{9\times8}{8} \\ p(\frac{3}{4})=\frac{63}{8}-\frac{72}{8} \\ p(\frac{3}{4})=\frac{63-72}{8} \\ p(\frac{3}{4})=\frac{63-72}{8} \\ p(\frac{3}{4})=\frac{-9}{8} \\ p(\frac{3}{4})=-\frac{9}{8} \end{gathered}[/tex]
Then, th answer is:
[tex]p(\frac{3}{4})=-\frac{9}{8}[/tex]
