1.8 Quadratic Formula.notebook
September 27, 2016
Warm Up
Simplify....
1. (3 + 4i) - (5 - 4i)
4
3
4. 9i -8i
71
2. (-2+i)
-6i
3. i
5. (5 +3i)(6 - 7i)
6. 3i(4+2i)
Solve by completing the square.
2
7. 4x - 8x = 1
Answers
1.
2.
3.
4.
5.
6.
7.
±
8.
9.
±
10.
11.
±
12.
Oct 11­2:53 PM
1
1.8 Quadratic Formula.notebook
September 27, 2016
1.8 Quadratic Formula
quadratic formula:
To use the quadratic formula:
1. Equation must be in the form ax2 +bx + c = 0.
2. Identify the values of a, b, and c.
3. Plug the values of a, b, and c into the formula.
4. Simplify the radical.
5. Simplify the answer.
Quadratic formula
Example: 2x2 ­ 3x ­ 2 = 0
example
2
1.8 Quadratic Formula.notebook
September 27, 2016
Example: 4x2 = 12x ­ 9
example
Example: 3x2 + 2x = 3
example
3
1.8 Quadratic Formula.notebook
September 27, 2016
Example: 5x2 + 2x + 1 = 0
example
Discriminant (b2 ­ 4ac)
From the discriminant, we can determine:
1. the number of roots or solutions (how many? 1 or 2?)
2. the type of roots or solutions (real or imaginary?)
discriminant
4
1.8 Quadratic Formula.notebook
2 real roots/solutions
September 27, 2016
1 real root/solution
2 imaginary roots/solutions
discriminant activity
Summary
If the value of the Then the roots or
discriminant is: solutions are:
1. 0 1. one real
2. positive 2. two real
3. negative 3. two imaginary
Examples: Without solving, find the value of the discriminant and describe the roots (number and type).
1. x2 ­ 3x ­ 40 = 0
2. 3x2 + 9x ­ 2 = 0
3. 7x2 + 6x + 2 = 0
4. x2 ­ 1/2x + 1/16 = 0
Oct 11­3:02 PM
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