y
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– 4321 Quadratics: Overview
Graphing
54321– 54321
.
y = (x – 1)2
x
The pattern & function is called a Quadratic
The resulting graph is called a parabola
The most basic parabola is y = x2
LEARN: From the vertex,
y
Across 1, up 1. Across 2, up 4. Across 3 up
9
16
x
y
15
y = x2
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-3
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2
1
-2
-1
0
1
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– 4321
54321– 54321
2
3
4
y = x2 + 3
x
-3
-2
-1
0
1
2
3
4
y
-3
-2
-1
0
1
2
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– 4321
54321– 54321
3
4
y = 2x
x
– 5– 4– 3– 2–– 11 y 1 2 3 4 5 x
–162
–153
–144
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5
4
3
2
1
– 5– 4– 3– 2–– 11
–2
–3
y
x
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-3
-2
-1
0
1
2
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4
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2
1
– 5– 4– 3– 2–– 11
–2
–3
–4
2
y
1 2 3 4 5 x
y
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5
4
3
2
1
– 5– 4– 3– 2–– 11
–2
–3
–4
1 2 3 4 5 x
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– 4321
54321– 54321
y
y = (x + 3)(x + 1)
x
-3
-2
-1
0
1
2
3
4
y
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2
1
– 5– 4– 3– 2–– 11
–2
–3
–4
.
Concepts
.
* Coordinates & plotting points
* Graphs with different axis scales
* Reading of values from a graph (given 'x' findy 'y' and vice
versa)
16 have points
* Understanding the context - should the graph
15
or a curve
* Plotting to introduce the idea of translation14
Vertical Translation
y = x2 + 1
y = x2 – 4
x
1 2 3 4 5 x
-3
-2
-1
0
1
2
3
4
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y
y
13
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5
4
3
2
1
– 5– 4– 3– 2–– 11
–2
–3
–4
1 2 3 4 5 x
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2
1
Horizontal translation
y = (x – 2)2
y = (x + 1)2
x
y
y
-3
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– 4321
54321– 54321
-2
-1
0
1
2
4
.
More Plotting
Inversion
y = - x2 + 4
x
-3
-2
-1
0
1
2
3
4
x
y
y
-1
0
1
2
2 3 4
5 x
3
4
Practice
x
-3
-2
-1
0
1
2
1 2 3 4 5 x
y
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– 4321
54321– 54321
-2
–162
–153
–144
. 13
12
11
10
9
8
7
6
5
4
3
2
1
– 5– 4– 3– 2–– 11
–2
–3
–4
y
-3
– 5– 4– 3– 2–– 11 y 1
3
y = ½ x2
Stretch
3
4
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y
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–2
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–3
14
–4
13
12
y = 2(x+1)2 + 3
11
10
9
y
8
7
6
5
4
3
2
1
– 5– 4– 3– 2–– 11
–2
–3
–4
y
1 2 3 4 5 x
1 2 3 4 5 x
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