How do I solve this problem?

Question

i have a problem on my precalculus homework. I’m having a rough time. It says “Find the power function that represents the points (5, 2), (7, 5) And (10, 9)”
please help me. I’m having a lot of trouble. Thanks!

Answer 1

Assuming (hopefully) the power function is a parabola.

2 = a(5 - h)² + k

5 = a(7 - h)² + k

9 = a(10 - h)² + k

 

Solve the system of three equations for a, h, and k