1. Solving Quadratic Equation by Graphing
Section 6.1

2. Quadratic Equation y = ax2 + bx + c ax2 is the quadratic term.
bx is the linear term.
c is the constant term.
The highest exponent is two; therefore, the degree is two.

3. Identifying Terms Example f(x)=5x2-7x+1 Quadratic term 5x2
Linear term x
Constant term 1

4. Identifying Terms Example f(x) = 4x2 - 3 Quadratic term 4x2
Linear term
Constant term

5. Identifying Terms Now you try this problem. f(x) = 5x2 - 2x + 3
quadratic term
linear term
constant term
5x2
-2x 3

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

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

8. Identifying Solutions
Example f(x) = x2 - 4
Solutions are -2 and 2.

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

10. 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.

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

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

13. Graphing Quadratic Equations
The graphing calculator is also a helpful tool for graphing quadratic equations.
Enter the equation in y1 on your calculator.