Thread: Finding 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?

Originally Posted by ManyTimes

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?

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.

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