I need to sketch the graph of t(x)=2x^2 +3x > or equal to 10x-x^2. How do I work out the points to plot on the graph?

Answer 1

one way: graph both functions and see where one is above the other. Visit

http://rechneronline.de/function-graphs/

and you can graph up to three functions at once. Set the y range for -20 to 20.

algebraic way:

2x^2+3x > 10x-x^2
3x^2 - 7x > 0
x(3x-7) > 0
either both factors are negative, or both are positive:
x is in (-∞,0) U (7/3,∞)