1. Lesson 5.6: The Quadratic Formula & the Discriminant
The Quadratic Formula is used to solve ANY quadratic equation.
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
To use the formula:
Equation must be in standard form
Equation must be equal to zero
Pick out a, b, & c
Plug & Chug

2. Solve using the quadratic formula.
1) 3 𝑥 2 +8𝑥=35
2) 2 𝑥 2 +𝑥= 𝑥 2 −3𝑥−4

3. 3) 3 𝑥 2 −6𝑥=5
4) −2 𝑥 2 =−2𝑥+3

4. The Discriminant is used to determine the number and type of solutions of a quadratic equation.
𝑏 2 −4𝑎𝑐=+# → 2 Real Solutions
𝑏 2 −4𝑎𝑐= → 1 Real Solutions
𝑏 2 −4𝑎𝑐=−# → 2 Imaginary Solutions

5. Determine the number and type of solution of each quadratic equation.
5) 9 𝑥 2 +6𝑥+1=0 6) 9 𝑥 2 +6𝑥−4=0 7) 9 𝑥 2 +6𝑥+5=0

6. HOMEWORK: p.295 #18-62 (EOE)