2.3 Solving Radical Equations Function EquationsRadical Equations Math 30-11.

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Presentation transcript:

2.3 Solving Radical Equations Function EquationsRadical Equations Math 30-11

Equations may be solved algebraically and graphically. Algebraic solutions sometimes produce extraneous roots. Graphical solutions are often approximate. Math 30-12

Math 20-1 Equations Containing One Radical Isolate the radical term on one side of the equation. Apply the Power Rule with squares to clear the square root. Determine the roots of the radical equation: Math 30-13

Terminology The solutions can be found by graphing the related function y = f(x). The roots of the equation are related to the zeros of the function or the x-intercepts of the graph. The solutions to an equation are also known as the roots of the equation. Can this equation be graphed to solve? The zeros of a function are located where the height of the graph of the function is zero. Math 30-14

Equation Function Function Graph x-intercepts solutions zeros roots Math 30-15

Solve Graphically Determine the zeros of the related function or Determine the x-intercepts of the graph of the related function. Method 1: Graph the LHS Graph the RHS Determine the point of intersection. The x-coordinate is the solution. Math 30-16

Solve Graphically Method 2: Zeros of the function. Rewrite to set equation = 0 Graph the related function. Determine the x-intercepts. The x-intercepts of the graph are related to the zeros of the function relates to the solution or roots of the equation. Math 30-17

Equations Containing One Radical Therefore the solution is x = 2. extraneous Math 30-18

Solve Graphically Method 1: x = 2 Method 2: x = 2 Math 30-19

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