What is the discriminant of a quadratic equation?

The discriminant of a quadratic equation $$ax^2 + bx + c = 0$$ is given by $$D = b^2 - 4ac$$ . It determines the nature of the roots.

What does a positive discriminant indicate?

A positive discriminant indicates that the quadratic equation has two distinct real roots.

What does a zero discriminant indicate?

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

What does a negative discriminant indicate?

A negative discriminant indicates that the quadratic equation has no real roots (the roots are complex).

How can you determine if a quadratic function is increasing or decreasing?

A quadratic function is increasing on the interval to the right of the vertex and decreasing on the interval to the left of the vertex.

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 of the parabola.

What is the effect of the coefficient $$a$$ in the quadratic function $$f(x) = ax^2 + bx + c$$ ?

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

What is a quadratic equation?

A quadratic equation is an equation that can be expressed in the standard form $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants and @@a eq 0@@.

Quadratic Functions Flashcard

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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 parabola?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

What does it mean for a quadratic function to have real roots?

Back

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