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

The range of a quadratic function that opens downwards is $$(-\text{∞}, k]$$ , where $$k$$ is the y-coordinate of the vertex.

How do you determine if a quadratic function has real roots?

A quadratic function has real roots if the discriminant, given by $$D = b^2 - 4ac$$ , is greater than or equal to zero.

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

The discriminant indicates 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 formula for the vertex of a quadratic function in standard form?

The vertex can be found using the formula $$\text{Vertex} = igg(-\frac{b}{2a}, figg(-\frac{b}{2a}igg)igg)$$ .

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

Changing the value of $$a$$ affects the width and direction of the parabola: if $$|a| > 1$$ , the parabola is narrower; if $$0

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

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

What is the effect of changing the value of $$c$$ in a quadratic function?

Changing the value of $$c$$ shifts the graph up or down along the y-axis.

How can you graph a quadratic function?

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

Quadratic Graphs and their key features 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 equation?

Back

3.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic graph?

Back

The vertex of a quadratic graph is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

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

Back

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