Expert: Sherry Wallin - 11/8/2009

Question
What is the function rule if  x = 5, 10, 15, 20 (that is the easy part) y = 10, 5, 10, 15. I can see that x is increasing by 5 each time, but y decreases by 5 then increases by 5.  Can you assist please?

Answer
Penny~
    Try plotting the ordered pairs (5,10), (10,5), (15,10), (20,15) to see what shape you get. I can tell you that you will get a parabola. You can plug values into the equation y = ax^2+bx + c using the 4 points and then solve a system of equations. I'm not sure what level you are studying but if you are in at least intermediate algebra you should be able to solve the resulting system of equations

10 = 5^2a + 5b + c
5 = 10^2a + 10b + c
10 = 15^2a + 15b + c
15 = 20^2a + 20b + c

this is 3 unknowns and 4 equations so it is doable. Also the vertex of the parabola is -b/2a when you find a and b and you know the parabola crosses the x axis when y = 0 and the y axis when x is 0.

Math Prof