quadratics part ii transformations. vertex form. fun. unit 4
TRANSCRIPT
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