Quadratic equation and Radical function

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The discussion focuses on finding radical and quadratic functions based on specific conditions. For the radical functions, the requirements include f(4)=0 and f(16)=6 for one function, and f(4)=0 and f(2)=2 for another. In the quadratic section, participants are tasked with determining functions based on vertex and intercept conditions, such as a vertex at (3,-1) and a vertical intercept at (0,8). The approach involves setting up equations based on the given points to solve for the constants in the function. Overall, the thread emphasizes the setup process for these mathematical problems rather than providing direct answers.
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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