Transcript 10.2 Solving Quadratics by Graphing

Solving Quadratic Equations
by Graphing
Lesson 10.2
Quadratic Solutions
The number of real solutions is at
most two.
6
f  x  = x 2 -2 x +5
6
2
4
4
-5
2
5
2
-2
5
5
-4
-2
-2
No solutions
One solution
Two solutions
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.
Identifying Solutions
2
Example y = x - 4
4
2
-5
-2
-4
Solutions are -2 and 2.
Identifying Solutions
Now you try this
problem.
4
2
l
2
y = 2x - x
5
-2
-4
Solutions are 0 and
Graphing Quadratic
Equations
The graph of a quadratic equation is
a parabola.
The roots or zeros are the xintercepts.
The vertex is the maximum or
minimum point.
All parabolas have an axis of
symmetry.
Graphing Quadratic
Equations
 One method of graphing uses a table with x values.
 Graph y = x2 - 4x
4
 Find the axis of symmetry 1st: -b








2a
Substitute the x = (a.o.s) into the equation,
solve for y.
This creates the ordered pair for the vertex.
Pick 2 x’s on each side of the vertex point to find
more points to graph the parabola.
The root(s) or solution(s) are where
the graph intercepts the x-axis.
 Axis of Symmetry x = 2
 Roots 0 and 4
Vertex (2, -4)
2
5
-2
-4
Graphing Quadratic Equations
 The graphing calculator is also a helpful tool
for graphing quadratic equations.
 Enter the equation into the graphing calculator.
 Graph to see how many roots the equation has.
 2nd Calc Zero to find each root.
 http://mathbits.com/MathBits/TISection/Alg
ebra1/Quadratic1.htm (1 and 3)
 You can also solve for the roots by factoring.