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Name:_______________________________

Period:____

Chapter 4 Notes Packet on Quadratic Functions and Factoring

Notes #15: Graphing quadratic equations in standard form, vertex form, and intercept form.

=

+

+

2

A. Intro to Graphs of Quadratic Equations:

y

ax

bx c

•

=

+

+ where

2

A ____________________ is a function that can be written in the form

y

ax

bx c

≠

=

= −

+

=

− −

2

2

2

a, b, and c are real numbers and a

0. Ex:

y

5

x

y

2

x

7

y

x

x

3

•

The graph of a quadratic function is a U-shaped curve called a ________________. The

maximum or minimum point is called the _____________

Identify the vertex of each graph; identify whether it is a minimum or a maximum.

1.)

2.)

Vertex: (

,

) _________

Vertex: (

,

) _________

3.)

4.)

Vertex: (

,

) _________

Vertex: (

,

) _________

=

+

+

2

B. Key Features of a Parabola:

y

ax

bx c

•

a > , the parabola opens ________:

Direction of Opening: When

0

a < , the parabola opens ________:

When

0

•

a < , the parabola is _______________ than

=

2

Width: When

1

y

x

a = , the parabola is the ________ width as

=

2

When

y

x

1

a > , the parabola is ________ than

=

2

When

1

y

x

•

Vertex: The highest or lowest point of the parabola is called the vertex, which is on the axis of

−

b

=

x

symmetry. To find the vertex, plug in

and solve for y. This yields a point (____, ____)

2

a

−

b

=

•

x

Axis of symmetry: This is a vertical line passing through the vertex. Its equation is:

2

a

•

x-intercepts: are the 0, 1, or 2 points where the parabola crosses the x-axis. Plug in y = 0 and

solve for x.

•

y-intercept: is the point where the parabola crosses the y-axis. Plug in x = 0 and solve for y.

1

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