Solving quadratics by graphing notes

1. Solving Quadratic Equations
by Graphing

2. Quadratic Equation
y = ax2 + bx + c
2
ax 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. Quadratic Solutions
The number of real solutions is at most
two.
6
f( ( ⋅
x ) x 2 -2 x )
= +5
6
2
4
4
2 -5 5
2
-2
5
5
-4
-2
-2
No solutions One solution Two solutions

4. 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.

5. Identifying Solutions
2
4
Example f(x) = x - 4
2
-5
-2
-4
Solutions are -2 and 2.

6. Identifying Solutions
Now you try this
problem. 4
2
f(x) = 2x - x 2
5
-2
Solutions are 0 and 2. -4

7. 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.

8. Graphing Quadratic Equations
One method of graphing uses a table with arbitrary
x-values. 4
Graph y = x2 - 4x
2
x y
0 0 5
1 -3
2 -4 -2
3 -3
4 0
-4
Roots 0 and 4 , Vertex (2, -4) ,
Axis of Symmetry x = 2