Hello there!

F(x,y) = (s, -s² + 4s)

S(x,y) = (8 -4*t, t)

Given the two graphs F and S, find all intersections between them.

Suggestions?

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- March 1st 2010, 07:47 PMManyTimesFinding the intersection between two graphs
Hello there!

F(x,y) = (s, -s² + 4s)

S(x,y) = (8 -4*t, t)

Given the two graphs F and S, find all intersections between them.

Suggestions? - March 1st 2010, 08:29 PMMush
They intersect where F(x,y) = S(x,y).

i.e.

(s, -s² + 4s)=(8 -4*t, t)

i.e.

s = 8 - 4*t (1)

t = -s² + 4s (2)

These are a pair of simultaneous equations, so you should be able to solve them. (Hint: Start by substituting equation (2) into equation(1), and using the quadratic formula to solve for s. Once you've done that, substitute your values for s into equation (1) or (2) to get values for t. Then use these values of s and t in the graph equations to find the points. - March 2nd 2010, 06:31 AMManyTimes
http://i45.tinypic.com/166xaph.jpg

Of course I should be able to solve this "problem", it is fairly easy, but I am not? I have no idea on what to do! :)

So far:

I set them as functions;

f(x) = -s² + 4s

g(y) = 8-4t

Solve equations:

x= s

y = -x² + 4x

y = -(x² -4x + 4) +4

y = -(x-2)² +4

Second equation (g(y))

y = t

x = 8-4y

4y = -x+8

y = -1/4x+2

Then hmm what :)