What does the equation $$y = (x + 5)^2$$ represent?

The equation $$y = (x + 5)^2$$ represents a quadratic function that is translated left 5 units from the parent function $$y = x^2$$ .

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

The transformation $$f(x) = x^2 - 2$$ indicates a vertical translation down 2 units from the parent function $$y = x^2$$ .

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

The transformation $$f(x) = (x - 3)^2$$ indicates a horizontal translation right 3 units from the parent function $$y = x^2$$ .

What is the transformation of the function $$f(x) = \frac{1}{2}(x - 1)^2 + 3$$ ?

The function $$f(x) = \frac{1}{2}(x - 1)^2 + 3$$ is horizontally translated right 1 unit and vertically translated up 3 units.

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

The transformation $$f(x) = -x^2 + 4$$ indicates a reflection across the x-axis and a vertical translation up 4 units.

What is the effect of a coefficient less than 1 in front of a quadratic function?

A coefficient less than 1 compresses the graph vertically, making it wider compared to the parent function.

What does the transformation $$f(x) = \frac{1}{3}(x + 2)^2 - 1$$ indicate?

The transformation $$f(x) = \frac{1}{3}(x + 2)^2 - 1$$ indicates a horizontal translation left 2 units, a vertical translation down 1 unit, and a vertical compression.

What is the general form of a quadratic function?

The general form of a quadratic function is $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants.

What does the transformation $$f(x) = \frac{1}{2}(x + 4)^2 + 1$$ indicate?

The transformation $$f(x) = \frac{1}{2}(x + 4)^2 + 1$$ indicates a horizontal translation left 4 units, a vertical translation up 1 unit, and a vertical compression.

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

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Transformations of Parent Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for creating more complex functions through transformations.

2.

FLASHCARD QUESTION

Front

What is a vertical translation?

Back

A vertical translation shifts a graph up or down without changing its shape.

3.

FLASHCARD QUESTION

Front

What is a horizontal translation?

Back

A horizontal translation shifts a graph left or right without changing its shape.

4.

FLASHCARD QUESTION

Front

How do you translate a quadratic function up by 5 units?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the effect of the negative sign in front of a quadratic function?

Back

The negative sign reflects the graph of the quadratic function across the x-axis.

7.

FLASHCARD QUESTION

Front

Back

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