2. Solving Quadratic Equations (finding roots)

3. Example f(x) = x 2 - 4 By Graphing Identifying Solutions Solutions are -2 and 2.

4. EXAMPLE 3 Solve a quadratic equation in standard form Solve 2x 2 + 20x – 8 = 0 by completing the square. SOLUTION Write original equation. 2x 2 + 20x – 8 = 0 Add 8 to each side. 2x 2 + 20x = 8 Divide each side by 2. x 2 + 10x = 4 Add 10 2 2, or 5 2, to each side. x 2 + 10x + 5 2 = 4 + 5 2 Write left side as the square of a binomial. (x + 5) 2 = 29

5. Solving Quadratic Equations by Factoring

6. Solve by using he zero product property. 1)2)3)

7. To solve a quadratic equation if you can’t factor the equation: Make sure the equation is in the general form. Identify a, b, and c. Substitute a, b, and c into the quadratic formula: Simplify.

8. Solve a previous problem using the quadratic formula.

9. Descriminants can give us hints…

10. For the equation...... the discriminant There are no real roots as the function is never equal to zero The Discriminant of a Quadratic Function If we try to solve, we get The square of any real number is positive so there are no real solutions to Roots, Surds and Discriminant

11. Complex Conjugates and Division Complex conjugates-a pair of complex numbers of the form a + bi and a – bi where a and b are real numbers. ( a + bi )( a – bi ) a 2 – abi + abi – b 2 i 2 a 2 – b 2 ( -1 ) a 2 + b 2 The product of a complex conjugate pair is a positive real number.

12. Ex. Find the real and non-real roots of