1. Dispatch

2. Solving Quadratic Equations by Graphing
Standard: 21.0

3. Let’s Review Vocabulary
Roots
Equation
vertex
parabola
maximum
Line of Symmetry
Minimum
x-intercept
y-intercept

4. Graphing Quadratic Equations
The graph of a quadratic equation is a parabola.
The roots or zeros are the x- intercepts.
The vertex is the maximum or minimum point.
All parabolas have an axis of symmetry.

5. Solving Equations
When we talk about solving these equations, we want to find the value of x when y = 0. These values, are where the graph crosses the x-axis, are called the x-intercepts.
These values are also referred to as solutions, zeros, or roots.

6. Quadratic Solutions The number of real solutions is at most two.
Two solutions
No solutions
One solution

7. Identifying Solutions
Example x2 – 4 = 0
Solutions are -2 and 2.

8. Identifying Solutions
– x2 + 6x – 9 = 0
Solution is 3.

9. Identifying Solutions
Now you try this problem.
2x - x2 = 0
Solutions are 0 and 2.

10. Identifying Solutions
x2 + 4x + 8 = 0
No solution.

11. Graphing Quadratic Equations
One method of graphing uses a table with arbitrary
x-values.
Graph y = x2 - 4x
Roots 0 and 4 , Vertex (2, -4) ,
Axis of Symmetry x = 2 x y 1 -3 2 -4 3 4

12. Graphing Quadratic Equations
Try this problem x2 - 2x – 8 = 0.
Roots
Vertex
Axis of Symmetry x y -2 -1 1 3 4

13. Italy and Jorge like playing soccer
Italy and Jorge like playing soccer. If they kicked the ball represented by the equation x2 + 6x = 7, can you them solve the equation by graphing.