What is the significance of the coefficient 'a' in a quadratic function?

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the parabola; larger absolute values of 'a' result in a narrower parabola.

What is a vertical stretch in the context of quadratic functions?

A vertical stretch occurs when the value of 'a' in the function $$f(x) = ax^2$$ is greater than 1, making the parabola narrower.

What is the effect of adding a constant to a quadratic function?

Adding a constant to a quadratic function shifts the graph vertically. For example, $$f(x) = x^2 + 3$$ shifts the graph up by 3 units.

What is the formula for the quadratic formula?

The quadratic formula is used to find the roots of a quadratic equation and is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, given by $$b^2 - 4ac$$ , which 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, only complex roots.

math 2 graphing quadratic functions ch 3 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 parabola?

Back

The vertex of a parabola 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 vertex of a quadratic function in standard form?

Back

5.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

What does it mean for a parabola to open upwards?

Back

7.

FLASHCARD QUESTION

Front

What does it mean for a parabola to open downwards?

Back

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