Guidlenes for tansforming graphs

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SUMMARY

This discussion focuses on transforming parabolas, specifically using the general equation of a parabola, y - b = k(x - a)². Key points include the significance of parameters a and b in determining the vertex location and the role of k in defining the parabola's orientation and width. The conversation highlights the need for clear guidelines on how function modifications affect graph transformations, including inverting the parabola and rearranging the equation into standard quadratic form.

PREREQUISITES
  • Understanding of quadratic functions and their properties
  • Familiarity with the vertex form of a parabola
  • Knowledge of completing the square technique
  • Basic algebraic manipulation skills
NEXT STEPS
  • Research the effects of changing the coefficient k in the parabola equation
  • Learn how to complete the square for quadratic equations
  • Explore graphing techniques for parabolas and their transformations
  • Study the relationship between vertex form and standard form of quadratic equations
USEFUL FOR

Students studying algebra, educators teaching quadratic functions, and anyone looking to deepen their understanding of graph transformations in mathematics.

FiveAlive
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This is a little more open ended then most HW questions. I'm helping a friend with some HW and we need to transform a parabola. Ultimately we have to find the tangent line, vertex, ect but I'm failing to recall the rules on how to manipulate the parabola to be in the domain of the graph we need and the sharpness of the curvature.

Can anyone recommend a webpage that lays out the the guideline of how changing a function will change the graph? I remember a few things like changing X^2 to -X^2 will invert the parabola but I've been surfing the web for a bit and haven't found anything concise and I can't find my old textbook.

Thanking you in advance,
Linus
 
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The general equation of a parabola opening up or down is

y - b = k(x - a)2.

The a and b determine the location of the vertex at (a,b). k positive or negative determines opening up or down. k large or small determines whether the parabola is "skinny" or "fat".
 
Hey thanks so much. Any suggestions for how to rearrange y - b = k(x - a)^2 so it looks more like a quadratic equation?
 
Normally you want to take a quadratic equation and complete the square to write it this way. But go ahead and multiply it all out and add b to both sides and you will have y as a quadratic equation expressed in powers of x.
 
You're brilliant. Thanks again for the help.
 

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