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Module 9.4.9.5,9.6

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This document discusses solving radical equations through multiple steps: 1) Isolate the radical on one side of the equation and square both sides to eliminate the radical. 2) Radicals can also be cubed roots, requiring the same process of isolating the radical and squaring both sides. 3) Radical equations can also be solved by graphing each side as functions and finding the intersection point of the graphs. 4) Transformations of radical equations, such as changing coefficients, affect the graph by shifting it up or down (changing k) or left or right (changing h).

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Module 9 Topics 9.4, 9.5, and 9.6 Solving radical equations. To solve an equation of this type first isolate the radical on one side and then square both sides to eliminate the radical.
To solve the radical equation following the steps as listed in the previous slide. Be sure when to complete every side on both sides.
Lets try several more examples just to be sure you understand the multiple steps involved in solving these types of equations. Step # 1
Some times the radicals are not square roots but cubed roots. Here is an example.
Here are a few for you to try. Remember to check by plugging the number you get as a result back into the equation to see if it works.
Here are the solutions.
Solve radical equations by graphing To solve by graphing type each side of the equation into y1 and y2. Example : Now have the calculator find the intersection Of the two equations. Type the equation just As you see them above.
Continuing with the solution to the radical equation . So the solution for x would be 10. Check it to make sure it works in the original equation.
Transformations of radical equations. Define domain and range. Graph the following equations and state their domain and range.
Solutions Domain all real numbers greater than or equal to Zero, Range all real numbers greater than or equal to zero. Domain all real numbers greater than or equal to -2, Range all real numbers greater than or equal to 0. Doman all real numbers greater than or equal to -2, Range all real numbers greater than or equal to -3.
General form of a radical equation What affect does a have on the graph is it is positive or negative? What affect does increasing h or decreasing h have on the equation? How does +k and k affect the graph? Try graphing a few to come up with the answers. Use your graphing calculators.
Review all of Module 9 Simplifying Radicals Adding/Subtracting/Multiplying/Dividing Radicals Solving radical equations Graphing radical equations State domain and range of radical equations Application problems with radicals

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Module 9.4.9.5,9.6

  • 1. Module 9 Topics 9.4, 9.5, and 9.6 Solving radical equations. To solve an equation of this type first isolate the radical on one side and then square both sides to eliminate the radical.
  • 2. To solve the radical equation following the steps as listed in the previous slide. Be sure when to complete every side on both sides.
  • 3. Lets try several more examples just to be sure you understand the multiple steps involved in solving these types of equations. Step # 1
  • 4. Some times the radicals are not square roots but cubed roots. Here is an example.
  • 5. Here are a few for you to try. Remember to check by plugging the number you get as a result back into the equation to see if it works.
  • 6. Here are the solutions.
  • 7. Solve radical equations by graphing To solve by graphing type each side of the equation into y1 and y2. Example : Now have the calculator find the intersection Of the two equations. Type the equation just As you see them above.
  • 8. Continuing with the solution to the radical equation . So the solution for x would be 10. Check it to make sure it works in the original equation.
  • 9. Transformations of radical equations. Define domain and range. Graph the following equations and state their domain and range.
  • 10. Solutions Domain all real numbers greater than or equal to Zero, Range all real numbers greater than or equal to zero. Domain all real numbers greater than or equal to -2, Range all real numbers greater than or equal to 0. Doman all real numbers greater than or equal to -2, Range all real numbers greater than or equal to -3.
  • 11. General form of a radical equation What affect does a have on the graph is it is positive or negative? What affect does increasing h or decreasing h have on the equation? How does +k and k affect the graph? Try graphing a few to come up with the answers. Use your graphing calculators.
  • 12. Review all of Module 9 Simplifying Radicals Adding/Subtracting/Multiplying/Dividing Radicals Solving radical equations Graphing radical equations State domain and range of radical equations Application problems with radicals