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Understanding Quadratic Equations and Simplifying Radicals

This lesson focuses on evaluating expressions, solving equations, and mastering the simplification of radicals. Students will learn essential properties of radicals, including the product and quotient properties, and how to simplify radical expressions into their simplest forms. We will explore methods for solving quadratic equations by taking square roots, isolating terms, and handling challenges like rationalizing the denominator. Homework will cover practice problems, ensuring a solid grasp of these concepts. Prepare to enhance your algebra skills!

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Understanding Quadratic Equations and Simplifying Radicals

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  1. HW due Warm – up 10/29/09 Evaluate the expression. 1.) Solve the equation. 2.) 3.) 4.) 24, 8 -3, +3 0 no real root

  2. What’s HappeninToday • Warm Up • Questions on HW • A little bit about ‘Simplifying Radicals’ • How to solve Quadratic Equations by taking the Square Root

  3. 5.3: Solving Quadratics by taking Square Roots

  4. Properties of Radicals Product Property: The square root of a product equals the product of the square roots of the factors. HUH? Example: Quotient Property: The square root of a quotient equals the quotient of the square roots of the numerator and denominator. HUH? Example:

  5. Radicals are in SIMPLEST FORM when.. • No perfect square factors other than 1 are in the radicand. • No fractions are in the radicand. • No radicals appear in the denominator.

  6. EX:3 When you have a pair, bring the number out. Prime Factor 2 48 2 24 2 12 2 6 3

  7. EX:4 Simplify. When you have a pair, bring the number out. Prime Factor 45 3 3 15 5

  8. Let’s look at another type Can’t be simplified more Divide inside the radical.

  9. Let’s look at another type Simplify each part Write as two radicals

  10. Now let’s use this to solve some quadratic equations…… Write the original equation. Take the square root of both sides Isolate the squared term by subtracting 3 Simplify Isolate the x by dividing by -5 HOUSTON WE HAVE A PROBLEM!!!!!1

  11. We can’t have a radical in the denominator We need to rationalize the denominator. Multiply numerator and denominator by Simplify

  12. Write the original equation. Simplify Isolate the squared term by multiplying by 3 Isolate the x by subtracting 5 Take the square root of both sides BOO!

  13. Home WorkPage 267-268: #20-66 EVEN

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