Question

Graph the function. f(x) = 1/5x^2 + 2x - 4

Answer 1

The x-coordinate of vertex of parabola is,

`x=-(b)/(2a)`

Determine the vertex of parabola.

`\begin{gathered} x=-(2)/(2\cdot(-(1)/(5))) \\ =5 \end{gathered}`

Substitute 5 for x in the function to obtain the y-coordinate of vertex.

`\begin{gathered} f(5)=-(1)/(5)\cdot(5)^2+2\cdot5-4 \\ =-5+10-4 \\ =1 \end{gathered}`

So vertex of parabola is (5,1).

Determine the roots of the function.

`\begin{gathered} x=\frac{-2\pm\sqrt[]{(2)^2-4\cdot(-(1)/(5))\cdot(-4)}}{2\cdot(-(1)/(5))} \\ =\frac{-2\pm\sqrt[]{4-3.2}}{-0.4} \\ =(-2\pm0.894)/(-0.4) \\ \approx2.764,7.236 \end{gathered}`

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.