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Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities. Chapter 5 – Quadratic Functions and Inequalities 5.6 – The Quadratic Formula and the Discriminant. 5.6 – The Quadratic Formula and the Discriminant. In this section we will learn how to:

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Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities

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  1. Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.6 – The Quadratic Formula and the Discriminant

  2. 5.6 – The Quadratic Formula and the Discriminant • In this section we will learn how to: • Solve quadratic equations by using the Quadratic Formula • Use the discriminant to determine the number and type of roots of a quadratic equation.

  3. 5.6 – The Quadratic Formula and the Discriminant • Exact solutions to some quadratic equations can be found by graphing, factoring or by using the Square Root Property. • Completing the square can be used to solve any quadratic equation, but it can be tedious if the equations have fractions/decimals • Fortunately, a formula exists that can be used to solve any quadratic equation of the form ax2 + bx + c = 0

  4. 5.6 – The Quadratic Formula and the Discriminant • ax2 + bx + c = 0

  5. 5.6 – The Quadratic Formula and the Discriminant • Quadratic Formula • The solutions of a quadratic equation of the form ax2 + bx + c = 0, where a ≠ 0, are given by the following formula: • x=-b ± √b2-4ac 2a

  6. 5.6 – The Quadratic Formula and the Discriminant • Example 1 • Solve x2 – 8x = 33 by using the Quadratic Formula

  7. 5.6 – The Quadratic Formula and the Discriminant • Example 2 • Solve x2– 34x +289 = 0 by using the Quadratic Formula • When the value of the radicand is 0, there is only one rational root

  8. 5.6 – The Quadratic Formula and the Discriminant • Example 3 • Solve x2 – 6x + 2 = 0 by using the Quadratic Formula.

  9. 5.6 – The Quadratic Formula and the Discriminant • Example 4 • Solve x2 + 13 = 6x by using the Quadratic Formula

  10. 5.6 – The Quadratic Formula and the Discriminant • The expression b2 – 4ac is called the discriminant • The value of the discriminant can be used to determine the number and type of roots of a quadratic equation.

  11. 5.6 – The Quadratic Formula and the Discriminant

  12. 5.6 – The Quadratic Formula and the Discriminant • The discriminant can help you check the solutions of a quadratic equation. Your solutions must match in number and in type to those determined by the discriminant

  13. 5.6 – The Quadratic Formula and the Discriminant • Example 5 • Find the value of the discriminant for each quadratic equation. Describe the number and type of roots for the equation. • x2 + 3x + 5 = 0 • x2 – 11x + 10 = 0

  14. 5.6 – The Quadratic Formula and the Discriminant

  15. 5.6 – The Quadratic Formula and the Discriminant HOMEWORK Page 281 #15 – 45 odd

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