What is the vertex form of a quadratic function?

The vertex form of a quadratic function is $$f(x) = a(x-h)^2 + k$$ where (h, k) is the vertex.

How do you convert from standard form to vertex form?

To convert, complete the square on the quadratic expression in standard form.

What is the quadratic formula?

The quadratic formula is used to find the roots of a quadratic equation and is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What does the discriminant tell us?

The discriminant, given by $$b^2 - 4ac$$ , indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if

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

The maximum or minimum value occurs at the vertex and is equal to k in the vertex form $$f(x) = a(x-h)^2 + k$$ .

What is the range of a quadratic function?

The range depends on the vertex: if a > 0, range is [k, ∞); if a

How do you identify the axis of symmetry on a graph?

The axis of symmetry can be identified as the vertical line that passes through the vertex of the parabola.

What is the effect of changing the 'b' value in a quadratic function?

Changing the 'b' value affects the position of the vertex along the x-axis and the axis of symmetry.

Characteristics of Quadratic Functions 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 is the standard form of a quadratic function?

Back

3.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

4.

FLASHCARD QUESTION

Front

How do you find the vertex from the standard form?

Back

5.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

7.

FLASHCARD QUESTION

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, characterized by its U-shape.

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