1. Solving Quadratic Equation by Graphing
Section 6.1 and 6.2

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 real solutions
2 imaginary solutions (use quadratic formula or completing square to find)
One solution
Two solutions
Either 2 rational or 2 irrational (may need to use quadratic formula or completing the square to find)

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 (a + min, a – max)
The roots or zeros are the x-intercepts.
The vertex is the maximum or minimum point.
All parabolas have an axis of symmetry. (x = -b/2a)
Y-intercept = c (0, c)

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 , y-intercept (0, 0) x y 1 -3 2 -4 3 4

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

13. Graphing Quadratic Equations
The graphing calculator is also a helpful tool for graphing quadratic equations.
Enter equation into y1 and 0 in for y2
To find min/max – 2nd trace min or max (also known as the vertex)
To find roots – 2nd trace intersect and find where it crosses the x-axis.