1.) Lesson On Vertex and Axis Of Symmetry (A.O.S.)

2.) Assignment

Learning Objectives: Students will be able to find the vertex and A.O.S. of a quadratic function.

AgendaAgenda

CA STANDARDS8.0: Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. 9.0: Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions.

x

y

A quadratic functionquadratic function - has the form2 .y ax bx c

Has a U U -shaped graph called a parabolaparabola..

ExamplesExamples::2y x

2 4 5y x x The The lowestlowest or or highesthighest point on the point on the graph is called thegraph is called the vertexvertex..

Standard FormStandard Form

(0, 0) (-2, -1)

All All parabolasparabolas can be divided in half can be divided in half about the about the axis of symmetryaxis of symmetry..

xx = = 00 xx = = -2-2

Check for Understanding

What do you call the line that divided the parabola in half?

AOS: Axis of Symmetry

What do you call the lowest or the highest point on the parabola?

Vertex

Example 1:Example 1:22 8 6y x x

a.) a.) VertexVertex::

( )

2( )

2

2vxb

a

22( ) 8( ) 6vy

2

((xxvv, , yyvv))

((22, , -2-2))2(4) 16 6

b.) b.) Axis of symmetryAxis of symmetry::

xx = = 22

Same asSame as xxvv value of value of VertexVertex!!

Write this !

_____a_____b_____c

2-86

2 2

82

a.) a.) VertexVertex:: ((22, , -2-2))

b.) b.) Axis of symmetryAxis of symmetry:: xx = = 22

c.)c.) y-intercept y-intercept:: ((00, ), )66

x

yLet’s graph these !

Example 1:Example 1:22 8 6y x x

Example 2:Example 2:

a.) a.) VertexVertex::

( )

2( )

0

2vxb

a

Plug in x to find y!

23( 10)vy

1

((xxvv, , yyvv))

((00, , 11))0 1

b.) b.) Axis of symmetryAxis of symmetry::

xx = = 00

Same asSame as xxvv value of the value of the VertexVertex!!

Write this !

_____a_____b_____c

-301

23 1y x

0

3

Write this !a.) a.) VertexVertex:: ((00, , 11))

b.) b.) Axis of symmetryAxis of symmetry:: xx = = 00

c.)c.) y-intercept y-intercept:: ((00, ), )11

x

yLet’s graph these !

x = 123(1) 1y

2y

(1, -2)(1, -2)

Same as vertex !!!Same as vertex !!!

Let’s create another point !!!Let’s create another point !!!

Example 2:Example 2:23 1y x

You Try:You Try:

a.) a.) VertexVertex::

( )

2( )

1

2vxb

a

Plug in x to find y!

23( ) )1 16( 2vy

1

((xxvv, , yyvv))

((11, , -1-1))3(1) 6 2

b.) b.) Axis of symmetryAxis of symmetry::

xx = = 11

Same asSame as xxvv value of the value of the VertexVertex!!

Write this !

_____a_____b_____c

3-62

23 6 2y x x

63

You Try:You Try: Pencils Down !

a.) a.) VertexVertex:: ((11, , -1-1))

b.) b.) Axis of symmetryAxis of symmetry:: xx = = 11

c.)c.) y-intercept y-intercept:: ((00, ), )22

x

yLet’s graph these !

23 6 2y x x