comparisons and operations
Changing an equation


The figure gives a graphical representation of the equation:


In this task you will change the equation to obtain other equations the solutions of which have certain properties. You can make the changes by transformations (using the Comparisons and translations and Comparisons and stretching tools), by algebraic operations (using the Comparisons and algebraic operations tool), or by any other method.


Changing the right side: If possible, replace the right side of the equation by a different linear function and leave the left side as is to obtain new equations with the following properties:
  • An equation with two negative solutions. .1
    An equation with two positive solutions. .2
    An equation with no solutions. .3
    An equation with exactly one solution. .4
    An equation with two solutions, one of which is 5. .5
    An equation with solutions identical to those of the original equation. .6
    Changing the left side: Replace the left side of the equation with another quadratic function, and leave the right side as is to obtain equations with properties 1-6 above, if possible.
  • Changing both sides: Change both sides in the same way to obtain equations with properties 1-6 above, if possible.






  • Comparisons and translations
    Comparisons and stretching
    Comparisons and algebraic operations


    Comparisons and transformations
    Algebraic operations on comparisons
    Product = constant
    Changing an equation
    Changing an equation by adding a function
    Constructing inequalities
    Inequality: linear and quadratic
    Inequality: two quadratic functions
    Inequality: changing the solution
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