find the area of the region bounded by the graphs of the equations.

i know how the function looks like when graphed because i used a graphing calculator... but what does y=0 mean???

Hey asilvester635.

Setting y = 0 means that you are finding the solutions of when the function crosses the x-axis.

This is also known as finding the roots of the equation where f(x) = -x^2 + 3x = 0.

Finding roots to equations has many purposes.

how do i solve this??? like how do i find the area?? how do i go about solving this equation?

Start by factorizing the equation into (x-a)(x-b) = 0 and then use the fact that x = a and x = b are solutions to this equation since at least one term has to be 0 in order for the LHS to be zero.

i don't get it....

Take the integral bounded at the intersection points.

is the x-axis

so, you're looking for the area between the curve and the x-axis

note the curve intersects the x-axis when



... the zeros, and are the limits of integration.

thank you so MUCH!!!!!

so do i just straight up integrate the function? and then plug in the 3 and 0 into x?