1. 9-6 The Quadratic Formula and Discriminant

2. Writing Quadratic Equations in Standard Form
ax² + bx + c = 0
a, b, and c should be on the same side of the equal sign
a should always be positive
Ex. 3x² + 2x = -5
3x² + 2x + 5 = 0

3. If ax² + bx + c = 0 and a ≠ 0, then 𝒙= −𝒃± 𝒃 𝟐 −𝟒𝒂𝒄 𝟐𝒂
Quadratic Formula
If ax² + bx + c = 0 and a ≠ 0, then 𝒙= −𝒃± 𝒃 𝟐 −𝟒𝒂𝒄 𝟐𝒂

4. Solving using the Quadratic Formula
Use ax² +bx + c = 0 to substitute a, b, and c into
𝒙= −𝒃± 𝒃 𝟐 −𝟒𝒂𝒄 𝟐𝒂
**caution** if ‘b’ is negative (ax² - bx + c + 0), you will still need to use the negative sign from the equation. You will end up with a double negative (which will make ‘b’ positive)
**if ‘b’ is negative then: 𝑥= −−𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 = 𝑥= 𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

5. Examples
a) x² - 8 = 2x b) 2x² + 5x + 3 = 0

6. Discriminant The expression under the radical of the quadratic formula
b² - 4ac

7. Real Solutions of the Discriminant
# of Real Solutions
Graph
> 0
= 0
< 0

8. Examples
a) x² + 4x – 15 = b) 3x² - 7x = -5

9. Homework
Page 279
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