1. Do Now
Use the standard form of a quadratic equation to find the a, b and c of each equation.
ax2 + bx + c = 0
x2 – 6x + 10 = 0
2x2 + 3x + 4 = 0
x2 – 5x – 7 = 8

2. 3.4 Using the Quadratic Formula
Objective: analyze the discriminant to determine the number and type of solutions

3. You can analyze the discriminant of a quadratic equation to determine the number and type of solutions of the equation.

4. Examples: Analyzing the Discriminant
Find the discriminant of the quadratic equation and describe the type of solution of the equation. a. x2 – 6x + 10 = 0 b. x2 – 6x + 9 = 0 c. x2 – 6x + 8 = 0

5. Practice: Analyzing the Discriminant
Find the discriminant of the quadratic equation and describe the type of solution of the equation. 1. 4x2 + 8x + 4 = 0 2. ½x2 + x – 1 = 0

6. Practice: Analyzing the Discriminant
Find the discriminant of the quadratic equation and describe the type of solution of the equation. 3. 5x2 = 8x – x2 – 3x = 6

7. Practice: Analyzing the Discriminant
Find the discriminant of the quadratic equation and describe the type of solution of the equation. 5. 4x2 + 6x = – 9 6. –5x2 + 1 = 6 – 10x

8. The Quadratic Formula x2 + 3x – 5 = 0
Solve using the quadratic formula.
x2 + 3x – 5 = 0

9. Example: Solve using the quadratic formula.
x2 – 6x+9 = 0

10. Practice solving equations with the quadratic formula.
x2 + 2x – 3 = 0
2x2 + 4x – 1 = 0
3x2 – 2x – 6 = 0

11. Homework
Section 3.4 Practice A Worksheet

12. Do Now
Determine the number and type of solutions to the equation x2 + 7x = – 11
Two real solutions
One real solution
Two imaginary solutions
One imaginary solution