The x-coordinate of vertex of parabola is,
[tex]x=-\frac{b}{2a}[/tex]
Determine the vertex of parabola.
[tex]\begin{gathered} x=-\frac{2}{2\cdot(-\frac{1}{5})} \\ =5 \end{gathered}[/tex]
Substitute 5 for x in the function to obtain the y-coordinate of vertex.
[tex]\begin{gathered} f(5)=-\frac{1}{5}\cdot(5)^2+2\cdot5-4 \\ =-5+10-4 \\ =1 \end{gathered}[/tex]
So vertex of parabola is (5,1).
Determine the roots of the function.
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{(2)^2-4\cdot(-\frac{1}{5})\cdot(-4)}}{2\cdot(-\frac{1}{5})} \\ =\frac{-2\pm\sqrt[]{4-3.2}}{-0.4} \\ =\frac{-2\pm0.894}{-0.4} \\ \approx2.764,7.236 \end{gathered}[/tex]
Thus function intrsects the x axis at (2.764,0) and (7.236,0).
The function intersect the y-axis at (0,-4).
Plot the function on graph.
