What is the equation of a parabola that opens to the right?

The equation is $$y^2 = 4px$$ where p is the distance from the vertex to the focus.

How do you determine if a parabola opens upwards or downwards?

If the coefficient of $$y$$ in the equation $$x^2 = 4py$$ is positive, it opens upwards; if negative, it opens downwards.

What is the standard form of a parabola with vertex at the origin?

The standard form is $$y = ax^2$$ .

What does the value of p represent in the context of a parabola?

The value of p represents the distance from the vertex to the focus and the vertex to the directrix.

How can you find the focus and directrix from the equation of a parabola?

Convert the equation to the standard form and identify p.

What is the significance of the vertex in a parabola?

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Focus & Directrix with Vertex (0,0) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

The vertex is (0, 0).

2.

FLASHCARD QUESTION

Front

Back

The focus is (0, 7).

3.

FLASHCARD QUESTION

Front

Back

The directrix is y = -7.

4.

FLASHCARD QUESTION

Front

What is the general form of a parabola that opens upwards?

Back

5.

FLASHCARD QUESTION

Front

What is the relationship between the vertex, focus, and directrix of a parabola?

Back

The vertex (h, k) is halfway between the focus and the directrix.

6.

FLASHCARD QUESTION

Front

Back

p = 9.

7.

FLASHCARD QUESTION

Front

Back

It has a maximum value.

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