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Algebra 2: Section 5.1

Graphing Quadratic

Functions

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Definitions

Quadratic function

– Standard form

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( 0)

y ax bx c

a

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Parabola

–Graph of a quadratic function

–Looks like a “U”

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Definitions

Vertex

–Lowest or highest point of a

parabola

Axis of symmetry

–Vertical line that passes through the

vertex of a parabolic function

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Axis of

Symmetry

Vertex

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Vertex Form of Quadratic

Vertex Form Vertex:

(h, k)

Axis of

Symmetry:

x = h

2( )y a x h k

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Vertex Form of Quadratic

Vertex Form Direction:

– If a > 0, opens up

– If a < 0, opens down

Size:

– If a is a fraction between -1 and 1Wider

– If a is bigger than 1 or smaller than -1Narrower

2( )y a x h k

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Examples

Graph the quadratic function. Label the

vertex and axis of symmetry.

– Vertex: (-1, -4)

– Axis of Symmetry: x = -1

– Direction: Opens Up

– Size: Narrower

21. 2( 1) 4y x

2; 1; 4a h k

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Vertex: (-1, -4) Axis of Symmetry: x = -1

Direction: Opens Up Size: Narrower

21. 2( 1) 4y x

Graphing with Standard Form

Graph the quadratic function. Label the

vertex and axis of symm.

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22. 6 16y x x

29 ( 3) 16y x

2( 3) 7y x

2____ ( 6 ____) 16y x x 99

29 ( 6 9) 16y x x

6b 2

263 9

2c

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2( 3) 7y x

Vertex: ( 3,7)

Opens up

Standard Size

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Examples

23. 2 12 14y x x

218 2( 3) 14y x

22( 3) 4y x

2____ 2( 6 ____) 14y x x 918

218 2( 6 9) 14y x x

6b 2

26( 3) 9

2c

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Vertex: (3, 4)

Opens up

Narrower

22( 3) 4y x

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Using TI-83/84 to graph parabolas

Press Y=

enter equation into Y1

Hit Graph

Adjust window as

necessary

(use Zoom or Window)

Example: (3 7)( 1)y x x

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Using TI-83/84 to graph parabolas

To find vertex– Be sure you can view

the vertex in your current window

– Go to the CALC menu(press 2nd – TRACE)

– Choose MAX or Min

– Place cursor to left of vertex

– press ENTER

– Place cursor to right of vertex

– press ENTER

– Place cursor close to vertex

– press ENTER

Example: (3 7)( 1)y x x

Assignment

p.253

#20-37 all

(18 problems)

Math Journal

Sports

p.254 #52

(explain how you found these values)

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