The vertex form for a parabola is given below:

To complete the square, take the value next to the x term, divide by 2 and raise the number to the second power. In this case,. Then take value and add it to add inside the parenthesis and subtract on the outside. 

Now factor and simplify:

Fromt the values of h and k, the vertex is at 

The vertex form for a parabola is given below:

To complete the square, take the value next to the x term, divide by  and raise the number to the second power. In this case, . Then take value and add it to add inside the parenthesis and subtract on the outside. Remember to distribute before subtracting to the outside.

Now factor and simplify:

From the values of  and , the vertex is at 

The vertex form for a parabola is given below:

Factor the equation and transform it into the vertex form.

To complete the square, take the value next to the x term, divide by  and raise the number to the second power. In this case, . Then take value and add it to add inside the parenthesis and subtract on the outside. 

Now factor and simplify:

From the values of  and , the vertex is at 

The vertex form for a parabola is given below:

To complete the square, take the value next to the x term, divide by 2 and raise the number to the second power. In this case, . Then take value and add it to add inside the parenthesis and subtract on the outside. 

Now factor and simplify:

Fromt the values of  and , the vertex is at 

In order to determine which direction the parabola opens, we must first put the equation in standard form, which can be expressed in one of the following two ways:

If the equation is for  as in the first above, the parabola opens up if  is positive and down if is negative. If the equation is for as in the second above, the parabola opens right if is positive and left if is negative. Rearranging our equation, we get:

We can see that our equation is for , which means the parabola will open either left or right. The sign of the first term is negative, so this parabola will open to the left.

For the function

The parabola opens upwards if a>0

and downards for a<0

Because 

The parabola opens upwards.

The standard form for a parabola is in the form: 

The coefficient of the  term determines whether if the parabola opens upward or downward.  Since the  term in the function  is , the parabola will open downward.

Use the FOIL method to determine  in its standard form for parabolas, which is .  

Regroup the terms.

Since the coefficient of the  term is negative, the parabola will open downward.

The focus is above the vertex, which means that the parabola will open up

In order to determine which way this parabola, group the variables in one side of the equation.  Add  on both sides of the equation to isolate .

Because the equation is in terms of , the parabola will either open left or right.  Notice that the coefficient of the term is negative.

The parabola will open to the left.