Quadratic equation and Radical function

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Quadratic equation and Radical function!!!

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.
 

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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.
 

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