In a equation in the form:
[tex]y=ax^2+bx+c[/tex]
The maximum or minimum value is the value of the function when x is:
[tex]x=-\frac{b}{2a}[/tex]
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For the given function:
[tex]y=-2x^2-3x+4[/tex][tex]\begin{gathered} x=-\frac{(-3)}{2(-2)}=\frac{3}{-4}=-\frac{3}{4} \\ \\ f(-\frac{3}{4})=-2(-\frac{3}{4})^2-3(-\frac{3}{4})+4 \\ \\ =-2(\frac{9}{16})+\frac{9}{4}+4 \\ \\ =-\frac{18}{16}+\frac{9}{4}+4 \\ \\ =-\frac{9}{8}+\frac{18}{8}+\frac{32}{8} \\ \\ =\frac{41}{8} \\ \\ =5\frac{1}{8} \end{gathered}[/tex]Then , the maximum value of the given function is 5 1/8
