1. QUADRATIC EQUATIONS JOURNAL BY ANA JULIA ROGOZINSKI

2. Factoring Polynomials
1st step: Find the GCF if possible
2nd step: Multiply a and c
3rd step: Then find two numbers that add up to b and multiply to the product a times c gave you.
4th step: You need to put both numbers over a.
5th step: Reduce as much as possible.

3. Example 1: Example 3: Example 2:
3x²-15x+12=0 X²-5x+4=0
3x²-9x+24=0
x²-3x+8=0
-4,-1
1 1
X= 4, 1
-4 , -2
Example 2:
X= 4, 2
m²+11m+30=0 30 11
5 , 6
1 1
X= -5, -6

4. A Quadratic Function:
The Equation used for Quadratic Function is x= ax²+bx+c. They Graph parabolas. The Difference between a quadratic function and a linear function is that the graph of a quadratic function is a parabola, whereas the graph of a linear function is just a straight line, also you use the slope intercept form of a line in linear function which is y=mx+b and in Quadratic functions we use x= ax²+bx+c.

5. Examples:
Is this equation used for a Quadratic function or a linear function? 3x²+5x+11 ( A quadratic ,remember the a is squared.
Is y=mx+b formula used for linear or quadratic functions?
When you are given a graph with an image like this
you know that it is a linear function. But
When you are given an image like
you know it is a quadratic function.

6. Graphing a Quadratic Function
The Quadratic Graphing Formula is a(x+b)²+c=0.
A: changes steepness depending if the parabola is going up or down, if a is less than 0 the parabola will be going down and if a is greater than 0 the parabola will be going up. Also if a is greater it is more steeper and if a is less that 0 the the parabola is less steeper.
B: moves right or left, b units moves opposite if positive it goes left and if negative it goes right.
C: moves vertex up or down , C unit if it is positive it goes up and if it is negative it goes down.

7. Example 1: Example 3: Example 2:
y=x^2
y=x^2-2x+8
y=-.5x^2+2x
Example 3:
Example 2:

8. Solving a quadratic equation
by graphing it
1st step: Set the equation equal to zero 2nd step: Make a T-table
3rd step: Find the vertex x=b/2a
4th step: Then put your vertex solution on the x side of the table and add two more numbers
5th step: Solve them, then graph your Parabola
Find the x-values where it crosses the x-axis
A solution is a method or process of solving a problem which is a true statement

9. Example 1: Example 3: Example 2: Example 4:
Y=-x2 X=0
Example 2:
X=0
Example 4:
No SOLUTION

10. Solving Quadratic Equations
Using Square roots
1st step: Be sure that x² is by itself.
2nd step: Then make sure there is no longer x
3rd step: Square root both sides
4th step: reduce as most as possible
5th step: don’t forget your +or-

11. Example 1: Example 3: Example 2:
a² = 16
a= + or -4
Example 3:
3x²-75=
3x²= 75
x² = 25
x= +or - 5
Example 2:
m²+9=0
-9 -9
m²= -9
m= + or - 3

12. Solving Quadratic Equations
Using Factoring
 1st Step: Find your A, B, and C.
2nd Step: Multiply a times c
3rd Step: Then on the T-table on one side put the solution of a x c and on the other put b
4th Step: Then find 2 numbers that when being added sum to b and when being multiplied to the solution a times c gave you.
5th Step: Reduce as much as possible.

13. Example 1:
Example 2:
Example 3:

14. Solving a quadratic Equation Using Completing the square
1st Step: Get x² =1
2nd Step: Then you need to get C by itself
3rd Step: Complete the square ( First get a =1, then find b, divide b/2, square it b/2² and finally factor (x+b/2)² )
4th Step: Add (b/2)² to both sides
5th Step:Finally square root both sides and DON’T FORGET + or -

15. Example 1: Example 3: Example 2:
a²+2a-3= a²+2a=3
(a+1)²= 3+1
a+1= +or-2
A= 3, 1
m² -12m+26=0
m²- 12m =
m²- 12m =10 (m+6)² = 10 m-6= +or- 10
M= 6, +or- 10
Example 2:
x²+8x=9
(x+4)² = 25
x+4 = + or -5
X= 1, -9

16. Solving a quadratic equation Using the Quadratic Formula
The Quadratic Formula is x= -b +or-√b² - 4ac 2a
1st Step: Find your A, B, and C. 2nd Step: Fill in the formula with your numbers
3rd Step: SOLVE!
THE DISCRIMINANT IS :

17. Example 1: Example 2: X² -5X -6 =0 x= 5 +or- 25-4 (-6) 2 x= 5 +or- 4
3w²+5w-7=0
x= -5 +or- 5²-4 (3)(-7)
2(3)
x= -5 +or 6
x= -5 +or

18.     
Example 3: