What is the range of a quadratic function that opens downwards?

The range is all real numbers less than or equal to the y-coordinate of the vertex, expressed as $$(-\infty, k]$$ .

What is the maximum value of a quadratic function?

The maximum value occurs at the vertex of a downward-opening parabola and is equal to the y-coordinate of the vertex.

What is the minimum value of a quadratic function?

The minimum value occurs at the vertex of an upward-opening parabola and is equal to the y-coordinate of the vertex.

How do you determine the domain of a quadratic function?

The domain of a quadratic function is always all real numbers, expressed as $$(-\infty, \infty)$$ .

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

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, but does not change the direction of the parabola.

How can you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, x-intercepts, and y-intercept, then plot these points and draw a smooth curve through them.

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

The coefficients 'a', 'b', and 'c' affect the shape, position, and orientation of the parabola, influencing its width, direction, and vertex location.

Characteristics of Quadratic Functions Flashcard

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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 does the 'a' value in a quadratic function indicate?

Back

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