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