1. Warm Up  1.) Write 15x 2 + 6x = 14x 2 -12 in standard form. (ax 2 + bx + c = 0)  2.) Evaluate b 2 – 4ac when a = 3, b = -6, and c = 5.

2. 4.8 Use the Quadratic Formula and the Discriminant

3. Quadratic Formula  Let a, b, and c be real numbers such that a ≠ 0. The solutions of the quadratic equation ax 2 + bx + c = 0 are:  x = -b ± √b 2 – 4ac 2a

4. Example 1 – Solve an equation with two real solutions  Solve x 2 – 5x = 7

5. Example 2 – Solve an equation with one real solution  Solve 16x 2 – 23x = 17x - 25

6. Example 3 – Solve an equation with imaginary solutions  Solve x 2 – 6x + 10 = 0.

7. Warm Up  Use the given values in the quadratic formula to solve.  1.) a = 1, b = 3, c = -2  2.) a = 4, b = -12, c = 9

8. The Discriminant  b 2 – 4ac  Can be used to find the number and type of solutions.  If b 2 – 4ac > 0 there are two real solutions.  If b 2 – 4ac = 0 there is one real solution.  If b 2 – 4ac < 0 there are two imaginary solutions.

9. Example 4 – Use the discriminant  Find the discriminant of the quadratic equation and give the number and type of solutions of the equation.  A.) x 2 + 10x + 23 = 0  B.) x 2 + 10x + 25 = 0  C.) x 2 + 10x + 27 = 0

10. Assignment  Pg. 296 (3 – 8 all, 13 – 18 all, 31 – 33 all)