Solving Quadratic Functions: A Quick Guide

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SUMMARY

The discussion focuses on solving the function y = -3f(2-x) - 2, with participants questioning the interpretation of the "root function" and the transformations applied to the equation. Key points include the identification of vertical stretches and reflections, with a consensus that the transformation is vertical due to the positioning of the coefficient outside the bracket. Additionally, there is confusion regarding the correct notation for square roots, emphasizing the importance of clarity in mathematical expressions.

PREREQUISITES
  • Understanding of function transformations, including reflections and stretches.
  • Familiarity with the notation for square roots and function representation.
  • Basic algebraic manipulation skills to isolate variables.
  • Knowledge of quadratic functions and their properties.
NEXT STEPS
  • Study function transformations in detail, focusing on vertical and horizontal shifts.
  • Learn proper mathematical notation for square roots and other functions.
  • Practice isolating variables in equations to enhance algebraic skills.
  • Explore quadratic functions and their characteristics, including vertex and axis of symmetry.
USEFUL FOR

Students studying algebra, particularly those tackling function transformations and quadratic equations, as well as educators seeking to clarify common misconceptions in mathematical notation.

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Homework Statement



y=-3f(2-x)-2 for the root function...

Homework Equations





The Attempt at a Solution



If I am given a function like, y=-3f(2-x)-2 for the root function...

Do i factor out the negetive on the x?

Making it.. y=-3f(-(x-2)-2 . making a reflection on both the x/y axis's ? Or is that wrong?
 
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Simple yes/no answer? :)
 
I don't want to be rude, but I have no idea what you're trying to do. Is y = f(x)? Is your equation:

f(x) = 3f(2-x) - 2?

What are you trying to do with this?
 
"Yes, No" to what question? You titled this "Quick Quadratics Question", but there is no quadratic in the problem. You say you are given the "root" function -3(2- x)- 2. What do you mean by "root function"? and , as gb7nash aked what are you trying to do with it?
 
Perhaps the thing to do is to solve for x in terms of y? I don't fully understand this either. You could isolate x on the left and that might be what is being asked? Not sure? will look forward to the correct solution.
 
::: (sqrt)2(x-4) +1

Is this a horizontal or vertical stretch/compression?

I said it was a vertical, since its outside the bracket.
 
Nelo said:
::: (sqrt)2(x-4) +1

Is this a horizontal or vertical stretch/compression?

I said it was a vertical, since its outside the bracket.
Please stop using your (sqrt) notation, with parenthes around "sqrt". Put the parentheses around the expression whose square root you're taking. With your notation it's impossible to tell whether the +1 is inside the radical or outside.

Is this your function?
y = sqrt(2(x - 4) + 1)
 

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