**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.

y² = 4ax is the standard equation of the parabola which is 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.

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

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) + 4 ^{2} - 4^{2} = 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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