Translations of Quadratic Functions

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 2 units

• Translate right 2 units

• Translate down 2 units

• Translate left 2 units

Answer explanation

Vertex of f(x): (0, 0)

Vertex of g(x): (0, -2)

From (0, 0) to (0, -2), we must translate/shift/move down two units.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 4 units

• Translate right 4 units

• Translate down 4 units

• Translate left 4 units

• Translate down 5 units

Answer explanation

Vertex of f(x): (4, - 5)

Vertex of g(x): (0, - 1)

From (4, - 5) to (0, - 1), we must translate/shift/move left four AND up 4 units.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 4 units

• Translate right 4 units

• Translate down 6 units

• Translate left 4 units

• Translate left 5 units

Answer explanation

Vertex of f(x): (- 1, 4)

Vertex of g(x): (- 5, - 2)

From (- 1, 4) to (- 5, - 2), we must translate/shift/move left four AND down 6 units.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 2 units

• Translate right 2 units

• Translate down 2 units

• Translate left 2 units

Answer explanation

Vertex of f(x): (0, 0)

Vertex of g(x): (- 2, - 2)

From (0, 0) to (-2, -2), we must translate/shift/move left 2 AND down 2 units.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 4 units

• Translate right 3 units

• Translate down 4 units

• Translate left 3 units

• Translate left 4 units

Answer explanation

Vertex of f(x): (0, 0)

Vertex of g(x): (-3, -4)

From (0, 0) to (-3, -4), we must translate/shift/move left 3 AND down 4 units.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 5 units

• Translate right 1 unit

• Translate down 4 units

• Translate right 2 units

• Translate right 3 units

Answer explanation

Vertex of f(x): (2, -4)

Vertex of g(x): (3, 1)

From (2, -4) to (3, 1), we must translate/shift/move right 1 AND up 5 units.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 1 unit

• Translate right 1 unit

• Translate down 1 unit

• Translate left 1 unit

Answer explanation

Vertex of f(x): (0, 0)

Vertex of g(x): (1, 0)

From (0, 0) to (1, 0), we must translate/shift/move right 1 unit.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 1 unit

• Translate right 5 units

• Translate down 1 unit

• Translate up 2 units

• Translate up 3 units

Answer explanation

Vertex of f(x): (5, 2)

Vertex of g(x): (5, 3)

From (5, 2) to (5, 3), we must translate/shift/move up 1 unit.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 4 units

• Translate right 4 units

• Translate down 4 units

• Translate down 5 units

• Translate left 4 units

Answer explanation

Vertex of f(x): (-1, -3)

Vertex of g(x): (-5, 1)

From (-1, -3) to (-5, 1), we must translate/shift/move left 4 and up 4 units.

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 1 unit

• Translate right 1 unit

• Translate down 1 unit

• Translate left 1 unit

Answer explanation

Vertex of f(x): (0, 0)

Vertex of g(x): (-1, 0)

From (0, 0) to (-1, 0), we must translate/shift/move left 1 unit.