A square is drawn with one of its sides on the line y = 10. The endpoints of this side lie on the parabola y = x^2 + 5x + 4. What is the area of that square?
We will use geogebra!
1)Enter in the input bar f(x)=x^2=5*x+4. The parabola will be drawn.
2)Enter in the input bar f(y)=10. The horizontal line will be drawn.
3)Find the points of intersection of the parabola and the line y = 10 by using the intersection tool. They will be labelled B and C.
4)Use B and C and the regular polygon tool to make a square with B and C as the bottom vertices of the square.
5)Check in the algebra pane what poly1 is.
We are done! Check that your construction looks like mine.
Now get this. This was posted on one of the most prestigious forums on earth. Loaded with super mathematicians and olympiad hopefuls. Only two people answered this and one of them got it wrong!
Now I know dozens of them could do this problem. But to them it is nothing but pure drudgery. You have to solve a quadratic and then use the distance formula, not a lot of fun. By using an interactive geometry program it is fun and you get the right answer.