A parabola is a U-shaped curve that is the graph of a quadratic function, represented by the equation $$y = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What is the range of a parabola that opens upwards?

The range of an upward-opening parabola is $$[k, \text{∞})$$ , where $$k$$ is the y-coordinate of the vertex.

What is the range of a parabola that opens downwards?

The range of a downward-opening parabola is $$(-\text{∞}, k]$$ , where $$k$$ is the y-coordinate of the vertex.

What are the x-intercepts of a parabola?

The x-intercepts (or roots) are the points where the parabola crosses the x-axis, found by solving the equation $$ax^2 + bx + c = 0$$ .

How do you determine the increasing and decreasing intervals of a parabola?

The increasing interval is to the right of the vertex, and the decreasing interval is to the left of the vertex.

What is the significance of the vertex in a parabola?

The vertex represents the maximum or minimum value of the quadratic function, depending on the direction the parabola opens.

What is the formula for finding the vertex of a parabola in standard form?

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

What is the effect of changing the value of $$a$$ in the equation of a parabola?

Changing the value of $$a$$ affects the width and direction of the parabola; larger absolute values of $$a$$ make the parabola narrower.

What is the relationship between the vertex and the axis of symmetry?

The vertex lies on the axis of symmetry, which is the line that divides the parabola into two equal halves.

Parabola Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a parabola?

Back

Tags

CCSS.HSF-IF.C.7A

2.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

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

3.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a parabola?

Back

4.

FLASHCARD QUESTION

Front

How do you find the y-intercept of a parabola?

Back

Tags

CCSS.HSF-IF.C.7A

5.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

What does it mean if a parabola opens upwards?

Back

Tags

CCSS.HSF-IF.C.7A

7.

FLASHCARD QUESTION

Front

What does it mean if a parabola opens downwards?

Back

Tags

CCSS.HSF-IF.C.7A

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