If $$f(x) = x^2$$ is transformed to $$g(x) = x^2 + 5$$ , what transformation has occurred?

The graph is shifted vertically upward by 5 units.

What does the transformation $$f(x) = (x - 1)^2 + 4$$ represent?

A horizontal shift right 1 unit and a vertical shift up 4 units.

What is the effect of a coefficient greater than 1 in front of $$x^2$$ in a quadratic function?

It vertically stretches the graph.

What is the effect of a coefficient between 0 and 1 in front of $$x^2$$ in a quadratic function?

It vertically compresses the graph.

How do you identify a horizontal shift in a quadratic function?

Look for changes in the x-term inside the parentheses, such as $$(x - h)$$ or $$(x + h)$$ .

What does the transformation $$f(x) = (x + 2)^2 - 3$$ indicate?

A horizontal shift left 2 units and a vertical shift down 3 units.

If $$f(x) = (x - 4)^2 + 1$$ , what are the transformations compared to the parent function?

Shift right 4 units and up 1 unit.

What is the significance of the vertex in a quadratic function?

The vertex represents the highest or lowest point of the parabola, depending on its orientation.

Transformations of Quadratic Functions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the parent function of a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

Back

The function is shifted horizontally by h units and vertically by k units.

3.

FLASHCARD QUESTION

Front

Back

It indicates a vertical shift upward by k units.

4.

FLASHCARD QUESTION

Front

Back

It indicates a vertical shift downward by k units.

5.

FLASHCARD QUESTION

Front

Back

It shifts the graph 3 units to the left.

6.

FLASHCARD QUESTION

Front

Back

It shifts the graph 2 units to the right.

7.

FLASHCARD QUESTION

Front

Back

It results in a horizontal shift in the opposite direction.

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