What is the vertex of the parabola represented by the equation $$ (y-4)^2=-8(x+1) $$ ?

The vertex is the point where the parabola changes direction. For the equation $$ (y-4)^2=-8(x+1) $$ , the vertex is at the point (-1, 4).

What is the equation of the directrix for the parabola given by $$ (x+3)^2 = 4(y+5) $$ ?

The directrix is a line that is perpendicular to the axis of symmetry of the parabola. For the equation $$ (x+3)^2 = 4(y+5) $$ , the directrix is given by the equation y = -6.

In which direction does the parabola represented by the equation $$ (y-9)^2=-40(x+4) $$ open?

The parabola opens to the left because the coefficient of $$ (y-9)^2 $$ is negative.

What does 'p' represent in the equation $$ (y-9)^2=-40(x+4) $$ ?

In the equation $$ (y-9)^2=-40(x+4) $$ , 'p' represents the distance from the vertex to the focus or directrix. Here, p = -10.

What is the standard form of a parabola that opens to the left?

The standard form of a parabola that opens to the left is $$ (y-k)^2 = -4p(x-h) $$ , where (h, k) is the vertex.

How do you find the vertex from the standard form of a parabola?

The vertex can be found directly from the standard form $$ y = a(x-h)^2 + k $$ as the point (h, k).

What is the axis of symmetry for the parabola represented by $$ y^2 = 4px $$ ?

The axis of symmetry for the parabola represented by $$ y^2 = 4px $$ is the x-axis (y=0).

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

The focus and directrix of a parabola are equidistant from any point on the parabola.

What is the significance of the value 'p' in the parabola's equation?

The value 'p' indicates the distance from the vertex to the focus and the vertex to the directrix.

How can you determine if a parabola opens upwards or downwards from its equation?

If the coefficient of $$ (x-h)^2 $$ in the equation $$ y = a(x-h)^2 + k $$ is positive, it opens upwards; if negative, it opens downwards.

What is the directrix of a parabola that opens upwards?

For a parabola that opens upwards, the directrix is given by the equation $$ y = k - p $$ , where (h, k) is the vertex.

What is the general form of a parabola's equation?

The general form of a parabola's equation is $$ y = ax^2 + bx + c $$ .

Focus, Vertex and Directrix of Parabolas Flashcards

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

Front

Which equation represents a right-facing parabola?

Back

5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

Front

Define the focus of a parabola.

Back

The focus of a parabola is a fixed point located inside the curve, where all the reflected rays converge.

7.

FLASHCARD QUESTION

Front

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

Back

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