Quadratics Part II

Transformations.Vertex form.

Fun.

Unit 4

LEARNING GOAL

• I can identify the effect of transformations on the graph of y = x2

Anatomy of a Parabola

Everything you ever wanted to know about a Parabola

The Most Basic Parabola

Parabolas on the Move

• You have the rest of the period to complete PARTS A, B, and C

• If you don’t finish in class, use this website to complete the rest tonight: http://goo.gl/YRsKt

• Other Homework: Skills Preparation for this Unit: p. 342 #1 ac, 4, 5, 6acegi, 7adfh, 8a, 9ce, 10b

Vertex Form

y = a(x – h)2 + k

y1= 2x2 + 3Vertex @

y = x2

x y

-4 16

-3 9

-2 4

-1 1

0 0

1 1

2 4

3 9

4 16

Transformations

Consolidate So far: How to graph a parabola from Vertex Form

• METHOD 1: POINT-BY-POINT from y=x2

• Choose a point on y=x2

• Keep the x co-ordinate the same• Change the y value: (y × a) + k• Move left or right by h• Choose another point and do it all over again!

y2= 3(x+2)2Vertex @

y = x2

x y

-4 16

-3 9

-2 4

-1 1

0 0

1 1

2 4

3 9

4 16

Transformations

Consolidate So far: How to graph a parabola from Vertex Form

• METHOD 2: STEP PATTERN• Identify the vertex• Plot the vertex• Use the step pattern to plot the rest of the

points from there (if a ≠ 1, then multiply each step by a)

y3= 3x2 - 4Vertex @

y = x2

x y

-4 16

-3 9

-2 4

-1 1

0 0

1 1

2 4

3 9

4 16

Transformations

y4= 2(x-3)2Vertex @

y = x2

x y

-4 16

-3 9

-2 4

-1 1

0 0

1 1

2 4

3 9

4 16

Transformations

y5= (1/5)x2 + 1

y = x2

x y

-4 16

-3 9

-2 4

-1 1

0 0

1 1

2 4

3 9

4 16

Vertex @

Transformations

y6= (1/3)(x+1)2Vertex @

y = x2

x y

-4 16

-3 9

-2 4

-1 1

0 0

1 1

2 4

3 9

4 16

Transformations