1. 4.8 Quadratic Formula and Discriminant

2. Quadratic Formula Formula: x = -b ± √(b2 – 4ac) 2a
This formula can be used to solve any quadratic equation.
Equations must be written in standard form.
Identify: a = b = c =
When solving the formula use order of operations.

3. Examples:
Solve the equations below:
(Ex1) x2 + 3x = 2

4. Equation with One Solution
Solve the equation below:
(Ex2) 25x2 – 18x = 12x – 9

5. Equation with Imaginary Solution
Solve the equation below:
(Ex3) -x2 + 4x = 5

6. Discriminant Formula: b2 – 4ac
Discriminant informs you how many and what type of solutions there are to a quadratic equation.
Types of Solutions:
1) # > real solutions
2) # = real solution
3) # < imaginary solutions

7. Examples: How many solutions are there to the equation below?
x2 – 8x + 17 = 0

8. Determine if the equation has a real solution or an imaginary solution.
7x2 – 2x = 5