Quadratic equation and Radical function

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SUMMARY

The discussion focuses on solving problems related to radical functions and quadratic functions. Specifically, the user seeks guidance on constructing radical functions with specified outputs and quadratic functions based on given vertex and intercept conditions. The quadratic function setup involves using the standard form F(x) = Ax² + Bx + C, with equations derived from provided points to determine the constants A, B, and C. The user emphasizes the need for assistance in setting up these functions rather than finding direct answers.

PREREQUISITES
  • Understanding of radical functions and their properties
  • Knowledge of quadratic functions and their standard form
  • Ability to solve systems of equations
  • Familiarity with vertex form and intercepts of quadratic equations
NEXT STEPS
  • Learn how to derive radical functions from given points
  • Study the vertex form of quadratic functions and how to convert between forms
  • Explore methods for solving systems of equations involving quadratic functions
  • Practice constructing quadratic functions from vertex and intercept information
USEFUL FOR

Students, educators, and anyone involved in algebra who seeks to deepen their understanding of radical and quadratic functions, particularly in problem-solving contexts.

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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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