What is the standard form of a quadratic function?

The standard form of a quadratic function is $$y = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants, and @@a eq 0@@.

What is the factored form of a quadratic function?

The factored form of a quadratic function is $$y = a(x - r_1)(x - r_2)$$ , where $$r_1$$ and $$r_2$$ are the roots (x-intercepts) of the function.

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 of the quadratic equation. If $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; and if $$D

How do you graph a quadratic function?

To graph a quadratic function, identify the vertex, axis of symmetry, y-intercept, and x-intercepts (if any). Plot these points and draw a smooth curve to form the parabola.

What is the relationship between the coefficients and the shape of the parabola?

The coefficient $$a$$ determines the direction of the parabola (upward if $$a > 0$$ , downward if $$a

What are the x-intercepts of a quadratic function?

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis. They can be found by solving the equation $$ax^2 + bx + c = 0$$ .

A parabola is the graph of a quadratic function. It is a U-shaped curve that can open upwards or downwards, depending on the sign of the leading coefficient $$a$$ .

How can you determine if a quadratic function opens upwards or downwards?

A quadratic function opens upwards if the leading coefficient $$a > 0$$ and opens downwards if $$a

Characteristics of Quadratics Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the range of a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

3.

FLASHCARD QUESTION

Front

How do you determine the increasing interval of a quadratic function?

Back

4.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

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

Back

A quadratic function has a minimum value if it opens upwards (a > 0) and the vertex represents the lowest point. It has a maximum value if it opens downwards (a < 0) and the vertex represents the highest point.

6.

FLASHCARD QUESTION

Front

What is the domain of a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

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

Back

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