1. Solving Quadratic Equations
By Graphing

2. Vocab review
Do you remember from unit 1?
Zeros
Zeros – the place where the graph crosses the x-axis
A.K.A – x-intercepts or Roots or solutions

3. How many solutions does a Quadratic have?
Sometimes is may have less than 2 solutions. Let’s see what that looks like.
Two solutions because the highest exponent is 2

4. How many solutions does a Quadratic have?
The graph crosses the x-axis twice
1 solution
The graph crosses the x-axis once
No solution
The graph never crosses the x-axis

5. How many solutions does a Quadratic have?
The graph crosses the x-axis twice
1 solution
The graph crosses the x-axis once
No solution
The graph never crosses the x-axis

6. Your turn! How many solutions do each of these graphs have? 1. 2. 3.
1 solution
2 solutions
2 solutions

7. Identifying the solutions from the graph
X = -2, 2
X = -3
X = -4, 1

8. You try! Identify the solutions from the graph X = -2, 2 No solution

9. Writing the equation from the graph.
Using the solutions from 2 slides ago
X = -2, 2
X = -3
X = -4, 1
Y = (x + 3)2
Y = -(x + 4)(x – 1)
Y = (x – 2)(x + 2)

10. You try! Write the equation of each graph. 1. 2. 3. Y = (x + 5)(x – 3)
Y = (x + 5)(x – 3)
Y = (x + 4)(x – 1)
Y = - (x – 4)2

11. Finding the solutions from a table
Ex: 1 x 1 2 3 4 5 6 y -2 -1
This table is of a Quadratic with 2 two solutions
Remember: The solution is also called a zero or x-intercept. Meaning that the y-coordinate of the solution is 0
These are my solutions
X = 5, 3

12. Finding the sol’n from a table cont.
Ex: 2 x -2 -1 1 2 3 Y 8
Find the solutions.
X = -1 and 1

13. Finding the sol’n from a table cont.
Ex: 3 x -2 -1 1 2 3 Y 16 9 4
Find the solutions.
This problem only has one solution
X = 2
Ex: 4 x -2 -1 1 2 3 Y 6 11
This problem no solution

14. Finding the sol’n from a table cont.
Ex: 5 x -2 -1 1 2 3 Y 12 5 -3 -4
Find the solutions.
This problem has two solution but only one is listed on the table
X = 0 , 4

15. Finding the solutions from a graph
There are zeros between -5 and -4 and between 1 and 2

16. Solutions from a table cont.
Ex: 6
Find the interval where the zero is. x 1 2 3 4 5 6 y -2 -7 -3
The zeros are between 2 and 3 and between 5 and 6