Goal: I can infer how the change in parameters

transforms the graph. (F-BF.3)

Unit 7 QuadraticsTranslating Graphs

2G1. y x

1. Compare graphs G1, G2 and G3. How have the graphs been affected?

2. Describe the effect of k on the equation f(x) = a(x – h)2 + k.

2G2. 2y x

Changing the 0 to a 2 moved the graph up 2.Changing the 0 to a -3 moved the graph down 3.

The k value shifts the graph up and down (vertically).

2G3. 3y x

2G4. 2y x

3. Compare graphs G1 and G4. How did changing x2 to (x+2)2 affect the graph?

4. Compare graphs G1 and G5. How did changing x2 to (x - 3)2 affect the graph?

5. Describe the effect of h on the equation.

2G5. 3y x

It shifts the graph to the left 2 spaces.

The h value shifts the graph right and left (horizontally).

2G1. y x

It shifts the graph to the right 3 spaces.

2G6. 2y x

6. Compare graphs G1 and G6. How did changing x2 to 2x2 affect the graph?

7. Compare graphs G1 and G7. How did changing x2 to ½x2 affect the graph?

8. Describe the effect of a on the equation.

21G7.2

y x

It makes the parabola more narrow.

The a value widens and narrows the parabola.

2G1. y x

It makes the parabola wider.

2G8. y x

9. Compare graphs G1 and G8. How did changing x2 to -x2 affect the graph?

10. Compare graphs G1 and G9. How did changing x2 to -3x2 affect the graph?

11. Describe the effect of a on the equation.

2G9. 3y x

It made the parabola open down instead of opening up.

The a value widens and narrows the parabola and determines the direction it will open.

2G1. y x

It made the parabola open down instead of opening up AND it made the parabola more narrow.

Example #1Describe and graph the transformation of

f(x) = x2 2( ) 2 3f x x

Transformations: Graph:Left 2 spacesDown 3 spaces

Example #2Describe and graph the transformation of

f(x) = x2 2( ) 1 4f x x

Transformations: Graph:Opens downRight 1 spaceUp 4 spaces

Example #3Describe and graph the transformation of

f(x) = x2 21( ) 22

f x x

Transformations: Graph:Opens downWideLeft 2 spaces

Translating Quadratic Graphs 2( )f x a x h k

a Opens Up/Opens DownNarrow/WideMoves left or rightMoves up or down

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