Notes 3.6 Quadratic Formula and the Discriminant.notebook
Bellwork
Solve the equation by completing the square.
2x2 + 8x + 3 = 0
October 24, 2014
Notes 3.6 Quadratic Formula and the Discriminant.notebook
Assignment 3.5b
October 24, 2014
Notes 3.6 Quadratic Formula and the Discriminant.notebook
October 24, 2014
Notes 3.6 Quadratic Formula and the Discriminant
Standard Form of a Quadratic
ax2 + bx + c = 0
If we complete the square...we get the Quadratic formula!
Notes 3.6 Quadratic Formula and the Discriminant.notebook
October 24, 2014
When we use the Quadratic Formula, we need to plug in a, b, and c!
x = Quadratic Formula Song (pop goes the weasel)
Quadratic Formula Song 2
(funny...slightly inappropriate)
Put the following into standard form and identify a, b and c:
1. 2 ­ x = 8x ­ x2
2. 3x2 + 5 = x2 ­ 4x
Notes 3.6 Quadratic Formula and the Discriminant.notebook
Review:
Solve by completing the square:
3. x2 ­ 2x ­ 18 = 0
October 24, 2014
We can do the same problem with the Quadratic Formula!
3. x2 ­ 2x ­ 18 = 0
Notes 3.6 Quadratic Formula and the Discriminant.notebook
October 24, 2014
Practice:
Solve using the Quadratic Formula:
4. 3x2 + 5x = 6
5. 5x2 + 3x = 4
Notes 3.6 Quadratic Formula and the Discriminant.notebook
October 24, 2014
discriminant
The expression b2 ­ 4ac under the radical is called the .
x = There are 3 cases, the discriminant could be positive, zero, or negative.
1. If b2 ­ 4ac is positive, the equation has real solutions.
2
2. If b2 ­ 4ac is zero, the equation has real solution.
1
3. If b2 ­ 4ac is negative, the equation has real solutions.
0
Notes 3.6 Quadratic Formula and the Discriminant.notebook
October 24, 2014
Use the discriminant to determine the number of real solutions of the quadratic equation.
6. 6x2 + 3x = ­4
7. 2x2 ­ x + 4 = 0
8. x2 = ­6x ­ 9
9. 3x2 + 5x ­ 6 = 0
Notes 3.6 Quadratic Formula and the Discriminant.notebook
October 24, 2014
DWA
1. What would the graph of a parabola with no real solutions look like?
Sample answer: The parabola would have a vertex above the x­axis and have a positive a value. This means it would point up and never cross the x­axis. It could also have a vertex that is below the x­axis and have a negative a value. This means it would point down and never cross the x­axis.