5.9.1 – The Quadratic Formula and Discriminant

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) = ax2 + bx + c

3. Example. Find the roots for the function f(x) = 2x2 + 5x - 7

4. Example. Find the roots for the function f(x) = x2 -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 • b2 – 4ac • The following cases could occur; • If b2 – 4ac > 0, two real solutions • If b2 – 4ac = 0, one real solution • If b2 – 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) x2 – 6x + 8 = 0 • B) x2 – 6x + 9 = 0 • C) x2 – 6x + 10 = 0

8. Example. Find the discriminant and solution(s) to the following quadratic using the quadratic equation. • f(x) = x2 + 2x + 3

9. Example. Find the discriminant and solution(s) to the following quadratic using the quadratic equation. • f(x) = x2 – 4x + 4

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