Algebra 1 CH 10.3 Solve Quadratic Equations by Graphing.notebook
Algebra 1 CH 10.3 Solve Quadratic Equations by Graphing.notebook
Solve Quadratic Equations by Graphing
April 30, 2015
Solve Quadratic Equations by Graphing
A quadratic equations looks like this: Objective: Graph quadratic equations and use the graphs to solve the equations.
or
Mar 2310:50 AM
Mar 2310:50 AM
Solve Quadratic Equations by Graphing Solve Quadratic Equations by Graphing
A quadratic equation can be written in the intercept form.
xintercepts
The xintercepts are p and q. x=5
x=4
Jul 184:17 PM
Jun 1511:46 AM
Solve Quadratic Equations by Graphing The axis of symmetry is half way between ( p, 0) and ( q, 0 ), and possesses the equation:
Solve Quadratic Equations by Graphing xintercepts
x=4
x=5
(0.5, 20.25)
Jun 1511:46 AM
Jul 184:17 PM
1
Algebra 1 CH 10.3 Solve Quadratic Equations by Graphing.notebook
Solve Quadratic Equations by Graphing
April 30, 2015
Solve Quadratic Equations by Graphing
Graph the following function.
Now find the axis of symmetry and the coordinates of the vertex.
What are the values of p & q?
q = 8 q = 8
p = 2 p = 2
Jun 1511:46 AM
Solve Quadratic Equations by Graphing
Jun 1511:46 AM
Solve Quadratic Equations by Graphing
each box = 2
Graph the following function:
p = 2
q = 8 What are p, q and the location of the vertex?
p = 4 p = 2
Jun 1511:46 AM
Solve Quadratic Equations by Graphing
q = 2 q = 8
Jul 184:17 PM
Solve Quadratic Equations by Graphing
Find the vertex.
Mar 2310:50 AM
Mar 2310:50 AM
2
Algebra 1 CH 10.3 Solve Quadratic Equations by Graphing.notebook
Solve Quadratic Equations by Graphing
April 30, 2015
Solve Quadratic Equations by Graphing
each box = 1/2
p = 4
q = 2
Jun 1511:46 AM
Solve Quadratic Equations by Graphing
x
8
4
1
0
1
2
4
f(x)
5
0
1.125
1
0.625
0
2
Jul 184:17 PM
Solve Quadratic Equations by Graphing
Two Solutions In the past, we talked about the degree of a function. We know that the degree tells us the maximum amount of solutions.
Mar 2310:50 AM
Solve Quadratic Equations by Graphing One Solution
Mar 2310:50 AM
Mar 2310:50 AM
Solve Quadratic Equations by Graphing No Solutions
Mar 2310:50 AM
3
Algebra 1 CH 10.3 Solve Quadratic Equations by Graphing.notebook
April 30, 2015
Solve Quadratic Equations by Graphing
Solve Quadratic Equations by Graphing
Statements that say a certain value is a : • zero • solution • xintercept
The following statements talk about the same concept.
These are very similar statements. This is the location where a graph of a parabola crosses the xaxis.
Zero: The zeros of a function occure when f(x)=0. For the function f(x)=x2+8x+15, the xintercepts are x = 3 and x = 5.
xintercept: the xintercepts occur when y=0. For the function y=x2+8x+15, the xintercepts are x = 3 and x = 5.
Solution: The solution of an equation occur when the equation is equal to zero. The solutions to x2+8x+15=0, are x = 3 and x = 5.
see page 646
Jul 184:17 PM
Jul 184:17 PM
Solve Quadratic Equations by Graphing
Objective: Graph quadratic equations and use the graphs to solve the equations.
Mar 2310:50 AM
4
Solve Quadratic Equations by Graphing
April 30, 2015
Solve Quadratic Equations by Graphing
A quadratic equations looks like this: Objective: Graph quadratic equations and use the graphs to solve the equations.
or
Mar 2310:50 AM
Mar 2310:50 AM
Solve Quadratic Equations by Graphing Solve Quadratic Equations by Graphing
A quadratic equation can be written in the intercept form.
xintercepts
The xintercepts are p and q. x=5
x=4
Jul 184:17 PM
Jun 1511:46 AM
Solve Quadratic Equations by Graphing The axis of symmetry is half way between ( p, 0) and ( q, 0 ), and possesses the equation:
Solve Quadratic Equations by Graphing xintercepts
x=4
x=5
(0.5, 20.25)
Jun 1511:46 AM
Jul 184:17 PM
1
Algebra 1 CH 10.3 Solve Quadratic Equations by Graphing.notebook
Solve Quadratic Equations by Graphing
April 30, 2015
Solve Quadratic Equations by Graphing
Graph the following function.
Now find the axis of symmetry and the coordinates of the vertex.
What are the values of p & q?
q = 8 q = 8
p = 2 p = 2
Jun 1511:46 AM
Solve Quadratic Equations by Graphing
Jun 1511:46 AM
Solve Quadratic Equations by Graphing
each box = 2
Graph the following function:
p = 2
q = 8 What are p, q and the location of the vertex?
p = 4 p = 2
Jun 1511:46 AM
Solve Quadratic Equations by Graphing
q = 2 q = 8
Jul 184:17 PM
Solve Quadratic Equations by Graphing
Find the vertex.
Mar 2310:50 AM
Mar 2310:50 AM
2
Algebra 1 CH 10.3 Solve Quadratic Equations by Graphing.notebook
Solve Quadratic Equations by Graphing
April 30, 2015
Solve Quadratic Equations by Graphing
each box = 1/2
p = 4
q = 2
Jun 1511:46 AM
Solve Quadratic Equations by Graphing
x
8
4
1
0
1
2
4
f(x)
5
0
1.125
1
0.625
0
2
Jul 184:17 PM
Solve Quadratic Equations by Graphing
Two Solutions In the past, we talked about the degree of a function. We know that the degree tells us the maximum amount of solutions.
Mar 2310:50 AM
Solve Quadratic Equations by Graphing One Solution
Mar 2310:50 AM
Mar 2310:50 AM
Solve Quadratic Equations by Graphing No Solutions
Mar 2310:50 AM
3
Algebra 1 CH 10.3 Solve Quadratic Equations by Graphing.notebook
April 30, 2015
Solve Quadratic Equations by Graphing
Solve Quadratic Equations by Graphing
Statements that say a certain value is a : • zero • solution • xintercept
The following statements talk about the same concept.
These are very similar statements. This is the location where a graph of a parabola crosses the xaxis.
Zero: The zeros of a function occure when f(x)=0. For the function f(x)=x2+8x+15, the xintercepts are x = 3 and x = 5.
xintercept: the xintercepts occur when y=0. For the function y=x2+8x+15, the xintercepts are x = 3 and x = 5.
Solution: The solution of an equation occur when the equation is equal to zero. The solutions to x2+8x+15=0, are x = 3 and x = 5.
see page 646
Jul 184:17 PM
Jul 184:17 PM
Solve Quadratic Equations by Graphing
Objective: Graph quadratic equations and use the graphs to solve the equations.
Mar 2310:50 AM
4
