**Table of Content (8 min. reading time)**

1 – Step by Step Solver: Find the Vertex of any Quadratic Equation

2 – How do you convert from Standard Form to Vertex Form?

3 – How do you locate the Vertex on the Graph of a Parabola?

4 – Example: How do you convert from Standard Form to Vertex Form?

5 – How do I find h and k in Vertex Form?

6 – What are h and k in Vertex Form?

### How do you convert from Standard Form to Vertex Form?

The Quadratic Equation in Standard Form isy=ax²+bx+cThen, the Vertex

**(h,k)**can be found from the above Standard Form using

h= -b/2a , k=f(h)Once computed, the vertex coordinates are plugged into the Vertex Form of a Parabola, see below.

#### Example: Convert from Standard Form to Vertex Form

Let’s converty=2x²+8x+3into Vertex Form.

Then,

**h = -b/(2a) = -(8)/(2*2) = -2**.

Next, compute k, the vertex y-coordinate, by plugging

**h = -2**

into

**k = 3*(-2)²+8(-2)+3 = -1**.

Thus, the vertex is

**(h,k)=(-2,-1)**.

Since -(-2)=2 we converted to the Vertex Form

y=(x+2)²-1.

Watch the video below for a great explanation of how to convert from Standard to Vertex Form.

### How do you locate the Vertex on the Graph of a Parabola?

Every Parabola has either a**minimum**(when opened to the top) or a

**maximum**(when opened to the bottom).

The Vertex is just that particular point on the Graph of a Parabola.

See the illustration of the two possible vertex locations below:

### Example: How do you convert from Standard Form to Vertex Form?

We are given the Standard Form

y=3x²- 6x-2.

First, compute the x-coordinate of the vertex

**h = – b/2a = -(-6) / (2*3) = 1**.

Next, compute the y-coordinate of the vertex by plugging h=1 into the given equation:

**k = 3*(1)²-6(1)-2 = -5**.

Therefore, the vertex is ** (h,k)=(1,-5) ** .

Thus, we transformed the above Standard Form into the Vertex Form

y=(x-1)²-5Easy, wasn’t it?

Tip: When using the above Standard Form to Vertex Form Calculator to solve

**3x²-6x-2=0** we must enter the 3 coefficients a,b,c as **a=3, b=-6, c=-2**.

Then, the calculator will find the Vertex ** (h,k)=(1,-5) ** Step by Step.

Finally, the Vertex Form of the above Quadratic Equation is

y=(x-1)²-5Get it now? Try the our Standard Form to Vertex Standard Calculator again.

### How do I find h and k in Vertex Form?

There are two ways to find h and k, the vertex x- and y- coordinates. There is a fast way and a long way.

1) The **fast** way: Given ** y = ax²+bx+c ** we first compute **h = -b / 2a ** and next ** k=f(h) ** .**Example:** ** y=3x²+6x+4 ** thus **h =-6/2*3 = -1 ** and **k = f(-1) = 3(-1)²+6(-1)+4 = 3-6+4 = 1 **

Thus, Vertex Coordinates are ** (k,h)=(-1,1) **.

2) The **long** way: We do the Complete-the-Square procedure to convert ** y=ax²+bx+c ** into ** y=a(x-h)²+k **.

We create a separate page to learn this method. Please click **HERE **to do this procedure.

### What are h and k in Vertex Form?

h and k are the Vertex x- and y- coordinates of the Graph of a Quadratic Equation. They give the Location of a Minimum (when a>0) or Maximum (when a<0).

You may also think of h and k as shifts/transformations:

Shifting the Standard Parabola**y=x²**

h units right yields**y=(x-h)²** .

Shifting it k units up yields**y=(x-h)²+k** .

By performing those 2 shifts we moved the Vertex from

the origin** (0,0)** to the new location ** (h,k)** .