How do you graph # y = (x-2)^2 +2#?
1 Answer
No
The general shape of the graph is
Explanation:
If your question wording 'how do you graph' were to be taken literally you would get the following answer:
Draw up a table of values by substituting for
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Assumption: You intend the question to be: Determine the important points of
Let any point on the graph be
Expanding the brackets of
As the coefficient of
Note that if the coefficient had been negative then you would have had the general shape of
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The given equation format is that of 'vertex form'
From this we can directly read off the vertex coordinates:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Set
Subtract 2 from both sides
Square root both sides
The square root of a negative number means that the graph does not cross the x-axis.
Where this is of complex number type of format:
'Real number' + 'Imaginary number'