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 Opens to the Right

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

Parabola Symmetric About X-axis and Opens to the Left

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

Parabola Symmetric About Y-Axis and Opens Up

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

Parabola Symmetric About Y-Axis and Opens Down

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

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 the direction it opens?

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 it opens?

y2 - 8y - x + 19 = 0

Solution :

Convert the given equation of  parabola 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.

Since X is positive, the parabola opens to the right.

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