### Concept (1)

In order to graph a parabola, we need to find several pieces of information, including the vertex. One way to find the vertex of a parabola is to turn the standard form of the quadratic equation into vertex form by completing the square. The primary difference between solving a quadratic by completing the square and putting an equation into vertex form is substituting a "y" for the "0" in the initial equation.

### Sample Problems (8)

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Find the vertex of:

y = x² − 4x + 6
###### Problem 1
How to find the vertex of a parabola by completing the square.

Find the vertex of:

f(x) = -2x² + 8x + 3
###### Problem 2
How to find the vertex of a parabola by completing the square with a negative leading coefficient.

Find the vertex of:

f(x) = ½x² + 3x + 4
###### Problem 3
How to find the vertex of a parabola by completing the square with a fractional leading coefficient.
###### Problem 4
Using completing the square to change from standard to vertex form when "a" is not one and "b" is even
###### Problem 5
Changing a parabola from standard to vertex form without completing the square
###### Problem 6
Using completing the square to change from standard to vertex form when "a" is not one and "b" is odd
###### Problem 7
Using completing the square to change a quadratic equation from standard for vertex form when "a" is one and "b" is even
###### Problem 8
Using completing the square to change a quadratic equation from standard for vertex form when "a" is one and "b" is odd