What does it mean for a quadratic function to have a maximum or minimum value?

A maximum value occurs at the vertex if the parabola opens downwards, while a minimum value occurs if the parabola opens upwards.

How do you determine the intervals where a quadratic function is positive or negative?

To find the intervals, identify the x-intercepts (roots) and test the sign of the function in the intervals defined by these roots.

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots: if $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

What is the vertex form of a quadratic function?

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

How can you convert from standard form to vertex form?

To convert, complete the square on the standard form $$f(x) = ax^2 + bx + c$$ to express it in the vertex form $$f(x) = a(x-h)^2 + k$$ .

What are the x-intercepts of a quadratic function?

The x-intercepts are the points where the graph intersects the x-axis, found by solving the equation $$ax^2 + bx + c = 0$$ .

What is the relationship between the coefficients and the graph of a quadratic function?

The coefficients $$a$$ , $$b$$ , and $$c$$ affect the shape, direction, and position of the parabola: $$a$$ determines the opening direction and width, $$b$$ affects the axis of symmetry, and $$c$$ is the y-intercept.

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

What is the axis of symmetry in a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

How do you find the y-intercept of a quadratic function?

Back

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