We can convert a quadratic equation from standard form to vertex form by “completing the square”.
Example: Find the vertex for the following quadratic relationships. Then draw a rough sketch of the graph.
a) =
+ 6 + 1
2
b) = 2
+ 4 − 2
2
c) = 2
+ 3 − 1
2
= 2
+ 10 + 12 without completing the square.
2
It is possible to find the vertex without completing the square. Find the vertex of the quadratic relationship given by