Graphs of Quadratic Functions Graph the function. Compare the graph with the graph of Example 1.
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Transcript of Graphs of Quadratic Functions Graph the function. Compare the graph with the graph of Example 1.
Graphs of Quadratic Functions
x y
Graph the function.Compare the graph with the graph of
Example 1
22 3y x
2y x
Graphs of Quadratic Functions
Practice 2
x y
Graph the function.Compare the graph with the graph of
23 6y x
Practice 1
x y
211
4y x
2y x
Solving Quadratics by Graphing.
2 2 8y x x
Look at the graph of the equation: What is the vertex of the graph?
( 1, 9)
What is the axis of symmetry of the graph?
1x
What are the x-intercepts of the graph?
( 4,0) and (2,0)
Does the graph open up or down?
up
What is the y-intercept of the graph?
(0, 8)
Solving Quadratics by Graphing.
The x-intercepts of
Example 2:
are ( 3,0) and (5,0)2 2 15y x x Find the vertex and sketch a graph of
2 2 15y x x
First, plot the intercepts.
What x-value falls half way between the intercepts?
This is the where the axis of symmetry lies.
It is also the x-value of the vertex.
Vertex:
1x
To find the y-value of the vertex, plug the x-value into the equation.
(1,16)
Plot the vertex. Plot the y-intercept.
Sketch the graph.
Solving Quadratics by Graphing.
The x-intercepts of
Practice 3:
are (1,0) and (7,0)
Find the vertex and sketch a graph of
2 8 7y x x
Vertex:
2 8 7y x x
Solving Quadratics by Graphing.
The real solutions to the quadratic equation 2 0ax bx c
are the x-intercepts of the graph of
Another name for solutions is roots.
2y ax bx c
We can use the graph of a quadratic function to find the solutions to the related equation.
Another name for x-intercepts is zeros.
Solving Quadratics by Graphing.
What are the solutions to the given quadratic equation?
4 or 2x x
2 2 8 0x x Example 3:
2 3 4 0x x Practice 4:
Solving Quadratics by Graphing.
Solve the equation by graphing.
2 6 8x x Example 4:
2 6 8 0x x
When solving a quadratic equation first write the equation in standard form: ax2 + bx + c = 0.
We will find the intercepts using our calculator.4 or 2x x
Whenever we solve a quadratic by graphing, we should sketch a graph of the function.
We will graph the related quadratic function.
2 6 8y x x
Solving Quadratics by Graphing.
Solve the equation by graphing.
Example 5:
1 or 6x x
2 5 6y x x
2 5 6 0x x Example 6:
22 6x x 22 6 0x x
22 6y x x
2 or 1.5x x
Solving Quadratics by Graphing.
Solve the equation by graphing.
Practice 5: 2 8 9 0x x
Practice 6: 2 11 12x x
Practice 7: 2 6 5x x
Solving Quadratics by Graphing.
Find the zeros of the function.
Example 7: 2( ) 4 5f x x x
Practice 8: 2( ) 4 12f x x x
Assignment: page 633: 25, 27, 30, 31 and page 647: 3-7, 18, 19, 22, 27, 28 ,31