How do you find the axis of symmetry for a quadratic function?

The axis of symmetry for a quadratic function in standard form $$f(x) = ax^2 + bx + c$$ is given by the formula $$x = -\frac{b}{2a}$$ .

What is the standard form of a quadratic function?

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

What is the difference between vertex form and standard form of a quadratic function?

Vertex form is $$f(x) = a(x-h)^2 + k$$ , which easily shows the vertex (h, k). Standard form is $$f(x) = ax^2 + bx + c$$ , which does not directly show the vertex.

What does it mean to reflect a graph over the x-axis?

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y). For example, $$f(x) = -x^2$$ reflects $$f(x) = x^2$$ .

How do you determine the direction of a parabola?

The direction of a parabola is determined by the coefficient 'a' in the quadratic function. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 it opens. It represents the maximum or minimum value of the function.

What is the formula for the vertex of a parabola given in standard form?

The vertex (h, k) of a parabola given in standard form $$f(x) = ax^2 + bx + c$$ can be found using $$h = -\frac{b}{2a}$$ and then substituting h back into the function to find k.

What does it mean to shift a graph left or right?

Shifting a graph left or right involves adding or subtracting a value from the x variable in the function. For example, changing $$f(x) = x^2$$ to $$f(x) = (x + 3)^2$$ shifts the graph 3 units to the left.

Quadratic Transformations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to translate a graph down 2 units?

Back

3.

FLASHCARD QUESTION

Front

How do you identify the vertex of a quadratic function in vertex form?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

What does it mean to stretch a quadratic function by a factor of 2?

Back

6.

FLASHCARD QUESTION

Front

Back

This transformation shifts the graph of the function 4 units to the right.

7.

FLASHCARD QUESTION

Front

Back

This transformation shifts the graph of the function 8 units up.

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