How Can Two Equations Have Multiple Points of Intersection?

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SUMMARY

The discussion centers on the intersection of the equations y = x^2 - x and y = x. The user correctly identifies one point of intersection at (0,0) by setting the equations equal to each other, resulting in x^2 - x = x, which simplifies to x^2 = 0. However, the user is confused by the answer book indicating a second intersection point at (2,2). The resolution lies in recognizing that the quadratic equation y = x^2 - x can yield multiple solutions, specifically at x = 0 and x = 2.

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  • Understanding of quadratic equations and their graphs
  • Familiarity with the concept of points of intersection
  • Basic algebraic manipulation skills
  • Knowledge of the Cartesian coordinate system
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  • Study the quadratic formula and its applications in finding roots
  • Learn how to graph quadratic functions and identify intersection points
  • Explore the concept of discriminants in quadratic equations
  • Investigate systems of equations and methods for solving them
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Students studying algebra, educators teaching quadratic functions, and anyone interested in understanding the graphical representation of equations and their intersections.

bob4000
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i have y=x^2-x and y=x

from this x^2-x=x
therefore: x^2=0, and x then equals zero.

putting this info into y=x, y=0

this gives the points (0,0). however, in the answer book, it shows that the points of intersection are (0,0) and (2,2). how is it possible to do this?!

appreciate any help or guidance

thanx
 
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dont worry about it just got confused

thnx
 

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