Aproblem that you will encounter in calculus 2 is finding the area under a curve. for the function f(x=-2x2-5x+3
a. find the x intercepts
b. describe how you would go about finding the area bounded by the x axis on the bottom and the x intercepts. calculus explanations not allowed.

-intercepts occur at points , so it follows that setting and solving for will give you the -coordinate of an intercept.



So the two intercepts are and . For values of between the two intercepts, say at , you have , which means the bounded region lies above the -axis.

The area of the bounded region is then given explicitly by the definite integral



Barring that (given your "no calc explanations allowed" caveat), the best you can do is to approximate the area of the region with basic shapes.