5. absolute value , sq , sq roots
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- 2. Absolute Value, Square Roots, and Quadratic Equations
- 3. Absolute value can be defined as the from zero on a number line. | 3 | is the point that is 3 units away from distance Zero
- 4. Geometrically: | x | = the distance of x from zero. Algebraically: x, for x > 0 | x | = -x for x < 0 Algebraically: x, for x > 0 | x | = -x for x < 0
- 5. Find | x | when x has the following values: -2, 5, .06, 0 , -⅞ x -2 5 .06 0 -⅞ | x |
- 6. Solve: | x - 3| = 5 can be read as "x is 5 units from 3 in either direction" Algebraically: | x - 3| = 5 means x -3 = or x -3 = Geometrically: eithe r -
- 7. Graph the points Use your calculator to complete the graph: The Absolute Value function is located in: Math> NUM>1: abs( Is f : x | x | a function? Create a table of values: x | x | 0 4 -4 9 -9 16 -16
- 8. The square root or sign stands for the square root of a real number. 4 stands for the positive value or Square Root radical The positive 2 To find the negative square root you need to write: - 4 which equals -2
- 9. 2 x Graph the points Use your calculator to complete the graph Complete the following table: x 0 4 -4 9 -9 16 -16
- 10. 8 6 4 2 -2 -4 -6 -10 -5 5 10 f x( ) = x y x= 8 6 4 2 -2 -4 -6 -10 -5 5 10 f x( ) = x 2 y x= 2 x What conclusion can you draw about the solutions to and | x | ?
- 11. Absolute Value- Square Root Theorem For all real numbers x, = | x | 2 x What does this mean? The square root of a squared expression is the as the absolute value of the expressionsame
- 12. Example 1 : Solve the following - 2 x = 72 | x | = 72 therefore: x = 72 or x = - 72 x = or x = - 2 72x =
- 13. Example 2: Solve the following - 34 2 12y− =
- 14. Example 3: Solve the following - 2 3 18x =
- 15. Example 4:Example 4: A square and a triangle have the same area. The triangle has base 7 cm. And altitude 6 cm. What is the length of a side of the square?
- 16. ClosureClosure • The |x| is – Geometrically: – Algebraically: • What can be said about • How do you solve |2y + 4| = 16? • How do you solve 4a2 = 28? 2 x and x
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