Quadratic equation and Radical function!!!

vt33

Please help with these two problems!!

1) a) Find a radical function where f(4)=0 and f(16)=6
b) Find a radical function where f(4)=0 and f(2)=2

2) a) find a quadratic function where the vertex is (3,-1) and has a vertical intercept of (0,8)
b)find a quadratic function where the X- intercepts are (3,0) and (-5,0) and has a vertical intercept of (0,-30)
c) Find a quadratic function where f(1) = 4,f(2)=6, and f(4)=22
I know it's a lot. I'm not looking for the answers, I just need to know how to set it up. Thanks in advance for anyone who chooses to assist me.

robert Ihnot

Well, anyway, in c) where you have the information to determine three constants, we set F(x) =Ax^2+Bx+C. F(1)=A+B+C=4; F(2) = 4A+2B+C=6; F(4)=16A+4B+C=22.