1. Solve x2 + 2x + 24 = 0 by completing the square.
Warmup
Solve x2 + 2x + 24 = 0 by completing the square.
A. –12, 12
B. –2, 2 C. D.

2. 3-6 The Quadratic Formula and the Discriminant
Goal: Solve quadratic equations by using the Quadratic Formula. Use the discriminant to determine the number and type of roots of a quadratic equation.

4. 15. Solve the equation by using the Quadratic Formula. 4 𝑥 2 −6=−12𝑥
4x2 + 12x − 6 = 0
a = 4, b = 12, c = -6
𝑥= −𝑏 ± 𝑏 2 −4𝑎𝑐 2𝑎
𝑥= −12 ± (12) 2 −4 4 (−6) 2(4)
𝑥= −12 ±
𝑥= −12 ±
𝑥= −12 ±
𝑥= −3 ±

5. The discriminant: 𝑏 2 −4𝑎𝑐; the value under the radical in the quadratic formula.
It helps you decide (discriminate between) how many solutions and what kind of solutions they will be.

6. KEY CONCEPT: DISCRIMINANT
Consider 𝑎 𝑥 2 +𝑏𝑥+𝑐=0, 𝑎≠0
Value of discriminant
Type and Number of Roots
Example of Graph of Related Function
𝑏 2 −4𝑎𝑐>0
2 real roots
𝑏 2 −4𝑎𝑐=0
1 real root
𝑏 2 −4𝑎𝑐<0
2 complex roots

7. Complete parts a-c for the quadratic equation.
Find the value of the discriminant
Describe the number and type of roots
Find the EXACT solutions by using the quadratic formula
𝑥 2 +5𝑥−1=0
End of Notes