adjusted

1. Solving
Quadratic Equations
by Graphing

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. 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.

4. The number of real solutions is at
most two.
Quadratic Solutions
No solutions
6
4
2
-2
5
f x  = x2-2 x +5
6
4
2
-2
5
2
-2
-4
-5 5
One solution Two solutions

5. Example f(x) = x2 - 4
Identifying Solutions
4
2
-2
-4
-5
Solutions are -2 and 2.

6. Example f(x) = 2x - x2
Solutions are 0 and 2.
Identifying Solutions
4
2
-2
-4
5

7. Vertex
When we are looking at real life examples like the motion of
a ball thrown in the air, you can use the graph of the
quadratic equation to gain information. We usually only
focus on the 1st quadrant. y
x
VertexThe max height of the ball
is 2 ft, and it reaches that
height after 1 sec.
The ball leaves the ground
at 0 sec and returns to the
ground after 2 sec.
Height
in ft
Time
in sec

8. Graphing a Quadratic Function
Remember, the steps to graphing a parabola in
standard form:
STEP 1: Find the Axis of symmetry using:
STEP 2: Find the vertex
STEP 3: Find two other points and reflect them across
the Axis of symmetry. Then connect the five points
with a smooth curve.
MAKE A TABLE
using x – values close to
the Axis of symmetry.
2
b
a
x 


9. 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.
Graphing Quadratic
Equations

10. Another 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
Graphing Quadratic
Equations
x y
0 0
1 -3
2 -4
3 -3
4 0
4
2
-2
-4
5