# What is the vertex form of #y= - x^2 - 10x + 20 #?

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.

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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'

Given:

Consider just the right hand side

write as

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write instead :

Multiplying

Using this to replace the brackets in expression (2)

We have gained the extra value of

so it is

However, it

Giving the final answer of

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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