# IDENTIFY THE DIRECTION A PARABOLA OPENS

## About "Identify the direction a parabola opens"

Identify the direction a parabola opens :

If the parabola is symmetric about x-axis, then we will have square for the variable y.So the given parabola will open upward or downward.

If the parabola is symmetric about y-axis, we will have square for the variable x.So the given parabola will open rightward or leftward.

## Parabola symmetric about x-axis and open rightward

y² = 4ax is the standard equation of the parabola which is symmetric about x axis and open rightward.

## Parabola symmetric about x-axis and open leftward

y² = -4ax is the standard equation of the parabola which is symmetric about x axis and open rightward.

## Parabola symmetric about y-axis and open upward

x² = 4ay is the standard equation of the parabola which is symmetric about y axis and open upward.

## Parabola symmetric about y-axis and open downward

x² = -4ay is the standard equation of the parabola which is symmetric about y axis and open downward.

Let us look into some example problems to understand the above concept.

Note : If the given parabola is not in the standard form, then we have to convert it into standard form and decide.

Example 1 :

From the given equation of the parabola, find in which direction does it open?

x² = - 16y

Solution :

The given parabola is having square for the variable x, it is symmetric about y-axis.

To decide in which direction does it open, we have to look into the sign.It has negative sign in front of 16y, so the parabola opens downward.

Example 2 :

From the given equation of the parabola, find in which direction does it open?

y² - 8y - x + 19 = 0

Solution :

Let us convert the given question in to standard form.

y² - 8y  =  x - 19

y² - 2y(4) + 42 - 42  =  x - 19

(y - 4)²  =  x - 19 + 16

(y - 4)²  =  x - 3

Let Y  =  y - 4 and X  =  x  - 3

Y²  =  X

Since the parabola is having square for the variable y, it is symmetric about X-axis.

It has positive sign, so the parabola opens rightward.

After having gone through the stuff given above, we hope that the students would have understood "Identify the direction a parabola opens".

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