6.4 Guided Notes Graphing Quadratic Functions Name: Date: Period:

[Pages:4]6.4 Guided Notes ? Graphing Quadratic Functions

Name: ______________________ Date: _____________ Period: ___

Objective: I can graph quadratic functions in standard form, vertex form, and factored form.

The graph of a quadratic function is called a ________________. There are ______ forms of quadratic equations:

() = 2 + +

() = ( ? )2 +

() = ( ? )( ? )

______________________

______________________

_____________________

If _____ is ______________ , the graph opens ________. If _____ is ______________ , the graph opens ________.

All quadratic equations have a ______________ which is the turning point of the graph. Quadratic graphs are symmetrical across the _____________________, which runs through the ______________. Formula:

A quadratic function crosses the y-axis ____________________ .

The y-intercept always has an x-value of ____. For a parabola, the y-intercept will be the point ( , )

A quadratic function crosses or touches the x-axis ___________ , ___________ , or ___________ times.

In this graph: Vertex: ____________ Axis of symmetry: ____________ Y-intercept is: ___________ X-intercepts are: ___________

Graphing in STANDARD FORM ? () = 2 + +

EXAMPLE - Graph the function: () = ? +

To find the axis of symmetry:

= - 2 =

=

=

To find the vertex, plug _______ back into the equation. (____) = ( ) ? ( ) + =

Key Features:

a = _______ b = _______ c = _______

The parabola will open UP or DOWN

The parabola has a

MAX or MIN

The axis of symmetry at = __________

Vertex at (

,

)

y-intercept = (

,

)

point = (

,

)

YOU TRY - Graph the function: () =

- + -

Key Features:

a = _______ b = _______ c = _______

The parabola will open UP or DOWN

The parabola has a

MAX or MIN

The axis of symmetry at = __________

Vertex at (

,

)

y-intercept = (

,

)

point = (

,

)

Graphing VERTEX FORM ? () = ( ? )2 +

The vertex is always the values of (, )

Find the vertex and "a":

1. () = 2( ? 2)2 + 4

vertex:

a:

2. () = -4( + 3)2 ? 5

vertex:

a:

3. () = -( - 1)2 ? 2

vertex:

a:

EXAMPLE - Graph the function: () = ( ? ) ?

Key Features:

a = _______

The parabola will open UP or DOWN

The parabola has a MAX or MIN

The axis of symmetry at = __________

Vertex at (

,

)

y-intercept = (

,

)

point = (

,

)

YOU TRY - Graph the function: () = -( + ) +

Key Features: a = _______

The parabola will open UP or DOWN

The parabola has a MAX or MIN The axis of symmetry at = __________

Vertex at (

,

)

y-intercept = (

,

)

point = (

,

)

Graphing in FACTORED FORM ? () = ( - )( - )

, are the _________________ also called the _________

and the axis of symmetry can be found using

+ 2

Find the x-intercepts and the axis of symmetry:

1. () = -3( - 1)( + 2)

2. () = ( + 3)( + 3)

x-ints: ( , ) a.o.s:

x-ints: ( , ) a.o.s:

( , )

( , )

3. () = -0.5( - 7)( + 1)

x-ints: ( , ) a.o.s: ( , )

EXAMPLE - Graph the function: () = -( ? )( ? )

Key Features:

a = _______

The parabola will open UP or DOWN

The axis of symmetry at = __________

Vertex at (

,

)

x-intercepts = (

,

)( ,

)

y-intercept = (

,

)

point = (

,

)

YOU TRY - Graph the function: () = ( + )( - )

Key Features:

a = _______

The parabola will open UP or DOWN

The axis of symmetry at = __________

Vertex at (

,

)

x-intercepts = (

,

)( ,

)

y-intercept = (

,

)

point = (

,

)

NOTE: For all quadratics, if you can find the vertex and one point, you can sketch the graph.

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