1. 5.9.1 – The Quadratic Formula and Discriminant

2. Recall, we have used the quadratic formula previously Gives the location of the roots (x-intercepts) of the graph of a parabola Function must be in standard form; f(x) = ax 2 + bx + c

3. Example. Find the roots for the function f(x) = 2x 2 + 5x - 7

4. Example. Find the roots for the function f(x) = x 2 - 2x - 4

5. All of the solutions we have covered though are real Possible to have imaginary roots = roots of the form a + bi Problem: cannot visualize the imaginary roots Still may find them algebraically

6. Since we cannot graph imaginary solutions, it can be difficult to tell what kind of solutions we could expect Discriminant = a way to determine the number(s) and type of solutions b 2 – 4ac The following cases could occur; If b 2 – 4ac > 0, two real solutions If b 2 – 4ac = 0, one real solution If b 2 – 4ac < 0, two imaginary solutions No mix and match

7. Example. Find the discriminant and given the number(s) and type of solutions for the following functions. A) x 2 – 6x + 8 = 0 B) x 2 – 6x + 9 = 0 C) x 2 – 6x + 10 = 0

8. Example. Find the discriminant and solution(s) to the following quadratic using the quadratic equation. f(x) = x 2 + 2x + 3

9. Example. Find the discriminant and solution(s) to the following quadratic using the quadratic equation. f(x) = x 2 – 4x + 4

10. Assignment Pg. 278 37-45 odd 51-59 odd