They can then determine the EXACT coordinates of the pts of intersection ALGEBRAICALLY for n=2,3 and k=2. You may want to go directly to the solution in terms of k. Some students will solve the system y=kx^2,x=ky^2 while others may recognize the advantage of solving y=kx^2,y=x. Strong discussion pts here including WHY (0,0) is always a solution.
7
Students can then derive the general form given below for the pts of intersection in terms of k and n. This requires stronger alg skills with exponents but again they should recognize that the system y=kx^n, y=x is much simpler.
8
9
10
11
12
1
6
13
0
2
14
15
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