What is the effect of a positive value added to the quadratic function, such as $$f(x) = x^2 + k$$ ?

Adding a positive value $$k$$ shifts the graph vertically upwards by $$k$$ units.

What is the effect of a negative value added to the quadratic function, such as $$f(x) = x^2 - k$$ ?

Subtracting a positive value $$k$$ shifts the graph vertically downwards by $$k$$ units.

How does the transformation $$f(x) = (x - h)^2$$ affect the graph?

This transformation shifts the graph horizontally to the right by $$h$$ units.

How does the transformation $$f(x) = (x + h)^2$$ affect the graph?

This transformation shifts the graph horizontally to the left by $$h$$ units.

What does the value of $$a$$ in the quadratic function $$f(x) = a(x - h)^2 + k$$ indicate?

The value of $$a$$ indicates the direction of the parabola: if $$a > 0$$ , it opens upwards; if $$a

What is the axis of symmetry for the quadratic function $$f(x) = a(x - h)^2 + k$$ ?

The axis of symmetry is the vertical line $$x = h$$ .

What is the maximum or minimum value of a quadratic function?

The maximum or minimum value occurs at the vertex of the parabola, depending on the direction it opens.

If a quadratic function has a maximum value, what can be said about the value of $$a$$ ?

If a quadratic function has a maximum value, then $$a

If a quadratic function has a minimum value, what can be said about the value of $$a$$ ?

If a quadratic function has a minimum value, then $$a > 0$$ .

What is the transformation of the function $$f(x) = (x + 7)^2$$ compared to the parent function?

This function represents a horizontal shift left by 7 units.

What is the transformation of the function $$f(x) = (x - 3)^2 - 7$$ compared to the parent function?

This function represents a horizontal shift right by 3 units and a vertical shift down by 7 units.

How can you determine the maximum or minimum value of a quadratic function from its graph?

The maximum or minimum value can be determined by identifying the vertex of the parabola on the graph.

Characteristics and Transformations of Quadratic Graphs Flashcards

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1.

FLASHCARD QUESTION

Front

What is the parent function of a quadratic?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to transform a quadratic function?

Back

Transforming a quadratic function involves shifting, stretching, compressing, or reflecting the graph of the parent function.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

The vertex of the function is the point (h, k).

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