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Chapter 9 – Quadratic Equations and Functions

Chapter 9 – Quadratic Equations and Functions. 9.2 – Simplifying Radicals. 9.2 – Simplifying Radicals. Today we will be learning how to: Use properties of radicals to simplify radicals Use quadratic equations to model real-life problems. 9.2 – Simplifying Radicals.

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Chapter 9 – Quadratic Equations and Functions

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  1. Chapter 9 – Quadratic Equations and Functions 9.2 – Simplifying Radicals

  2. 9.2 – Simplifying Radicals • Today we will be learning how to: • Use properties of radicals to simplify radicals • Use quadratic equations to model real-life problems

  3. 9.2 – Simplifying Radicals • Evaluate the radical expressions √ab and √a √bfor the given values of a and b. • a = 4, b = 9 • a = 25, b = 4 • a = 36, b = 16

  4. 9.2 – Simplifying Radicals • Evaluate the radical expressions for the given values of a and b. • a = 4, b = 49 • a = 16, b = 64 • a = 144, b = 100

  5. 9.2 – Simplifying Radicals • Product Property • The square root of a product equals the product of the square roots of the factors. • √ab = √a  √b where a ≥ 0 and b ≥ 0 • Ex. √4  100 = √4  √100

  6. 9.2 – Simplifying Radicals • Quotient Property • The square root of a quotient equals the quotient of the square roots of the numerator and denominator. • where a ≥ 0 and b > 0 • Ex.

  7. 9.2 – Simplifying Radicals • An expression is in simplest form if: • No perfect square factors other than 1 are in the radicand • √8 = √42 = 2√2 • No fractions are in the radicand • No radicals appear in the denominator of a fraction

  8. 9.2 – Simplifying Radicals • Example 1 • Simplify the expression √48

  9. 9.2 – Simplifying Radicals • Example 2 • Simplify the expression

  10. 9.2 – Simplifying Radicals • Example 3 • The distance d you can see to the horizon depends on your height h. A model is d2 = 1.5h, with d in miles and h in feet. • Find the exact distance you can see from the top of a 400 ft building.

  11. 9.2 – Simplifying Radicals • Example 3 • The distance d you can see to the horizon depends on your height h. A model is d2 = 1.5h, with d in miles and h in feet. • Find the distance in part 1 to the nearest tenth.

  12. 9.2 – Simplifying Radicals • Example 3 • The distance d you can see to the horizon depends on your height h. A model is d2 = 1.5h, with d in miles and h in feet. • If you were 3 × 400 = 1200 ft up in a skyscraper, how far could you see to the nearest tenth?

  13. 9.2 – Simplifying Radicals HOMEWORK Page 514 #10 – 48 even

  14. 9.2 – Simplifying Radicals HOMEWORK Page 514 #50 - 57

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