**How to graph a parabola in vertex form :**

The equation which is in the form

** y = **± a **(x - h) ^{2} + k**

known as vertex form of the parabola.

Here (h, k) stands for vertex.

To graph the above kinds of parabola, we need to find the following things.

(i) Find the axis of symmetry

(ii) Find the vertex of the parabola

(iii) x - intercept

(iv) y-intercept

**Axis of symmetry :**

The parabola is symmetric about the variable, which is not having square.

**Vertex of parabola :**

This point, where the parabola changes direction, is called the "vertex".

**x -intercept :**

The point where the parabola intersects the x-axis is known as x-intercept

To find the x-intercept, we have to put y = 0 and solve for x.

**y -intercept :**

The point where the parabola intersects the y-axis is known as x-intercept

To find the y-intercept, we have to put x = 0 and solve for y.

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

**Example 1 :**

Graph the following parabola

y = (x + 8)^{2} - 7

**Solution :**

**Axis of symmetry :**

In the above equation we don't have square for the variable y.

Hence the parabola is symmetric about y-axis.

The coefficient of (x + 8)^{2} is positive, the parabola opens upward.

Equation of axis ==> x = -8

**Vertex :**

y = (x + 8)^{2} - 7 ----(1)

y = a (x - h)^{2} + k -----(2)

By comparing the above equations, we get

(h ,k) ==> (-8, 7)

**x - intercept :**

Put y = 0

0 = (x + 8)^{2} - 7

(x - 8)^{2} = 7

x - 8 = √7

x = ±√7 + 8

x = √7 + 8 and x = -√7 + 8

**y - intercept :**

Put x = 0

y = (0 + 8)^{2} - 7

y = 64 - 7

y = 57

**Example 2 :**

Graph the following parabola

y = -2(x + 5)^{2} - 3

**Solution :**

**Axis of symmetry :**

In the above equation we don't have square for the variable y.

Hence the parabola is symmetric about y-axis.

The coefficient of (x + 5)^{2 }is negative, the parabola opens downward.

Equation of axis ==> x = -5

**Vertex :**

y = -2(x + 5)^{2} - 3 ----(1)

y = -a (x - h)^{2} + k -----(2)

By comparing the above equations, we get

(h ,k) ==> (-5, -3)

**x - intercept :**

Put y = 0

y = -2(x + 5)^{2} - 3

0 = -2(x + 5)^{2} - 3

-2(x + 5)^{2} = 3

x + 5 = -3/2

x + 5 = ±√(-3/2) (undefined)

**y - intercept :**

Put x = 0

y = -2(0 + 5)^{2} - 3

y = -2(5)^{2} - 3

y = -50 - 3 ==> -53

After having gone through the stuff given above, we hope that the students would have understood "How to graph a parabola in vertex form".

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