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Equations of Graph Translations

7.17.5 Equations of Graph Translations

7.17.5 • Equations of Graph Translations

Cool Down

1.

Here is a graph that represents f ( x ) = x 2 f ( x ) = x 2 .

A graph of the parent quadratic function is given in blue on the coordinate plane. The x-axis extends from negative 6 to 6 with a scale of 2. The y-axis extends from negative 30 to 30 with a scale of 10.

Use the graphing tool or technology outside the course. On the same coordinate plane, sketch a graph that represents f ( x ) = ( x − 6 ) 2 + 10 f ( x ) = ( x − 6 ) 2 + 10 .

Compare your answer:

A graph of the parent quadratic function is given in blue on the coordinate plane. The graph of a second parabola is given and labeled with a vertex at the point (6, 10).

A graph the same shape as f ( x ) = x 2 f ( x ) = x 2 but shifted 6 units to the right and 10 units upward. Its vertex is at ( 6 , 10 ) ( 6 , 10 ) .

2.

The graph representing f ( x ) = x 2 f ( x ) = x 2 is shifted 2 units to the left, 10 units down, and flipped so that it opens downward, as shown.

A coordinate plane displays a graph of the parent quadratic function in blue. Another parabola, graphed in black, was transformed using the parameters in the question. The x-axis extends from negative 6 to positive 6 with a scale of 2 while the y-axis extends from negative 30 to positive 30 with a scale of 10.

Which equation defines this curve?

a. f ( x ) = − ( x + 2 ) 2 − 10 f ( x ) = − ( x + 2 ) 2 − 10

b. f ( x ) = ( x + 2 ) 2 − 10 f ( x ) = ( x + 2 ) 2 − 10

c. f ( x ) = − ( x + 2 ) 2 + 10 f ( x ) = − ( x + 2 ) 2 + 10

d. f ( x ) = ( x + 2 ) 2 + 10 f ( x ) = ( x + 2 ) 2 + 10

f ( x ) = − ( x + 2 ) 2 − 10 f ( x ) = − ( x + 2 ) 2 − 10