What is the vertex form of #y= - x^2 - 10x + 20 #?
Vertex form of a parabola:
In order to put a parabola into vertex form, use the complete the square method.
Add the value that will cause the portion in parentheses to be a perfect square.
Since we added
Notice that the
This is the equation in standard form. It also tells you that the vertex of the parabola is
By using the vertex form (completing the square) you introduce an error. If this error is '+some value' then you correct by including '- the same value'
Consider just the right hand side
Write instead :
Using this to replace the brackets in expression (2)
We have gained the extra value of
so it is
Giving the final answer of