Given: #y=7x^2-9x-32#......................(1)
Write as:
#y=7(x^2-9/7x)-32#
Now write as
#y=7(x-[1/2xx9/7])^2-32 color(blue)(+"correction")#
#y=7(x-9/14)^2-32color(blue)(+"correction")#..........................(2)
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Consider #7(x-9/14)^2#
This gives: #7(x^2-9/7x+81/196)#
We need the #7(x^2-9/7x)# but the #7(+81/196)# is an extra value we need to get rid of. This is why we have a correction. In this case the correction value is:#color(blue)(7( -81/196)=-81/28)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So equation (2) becomes:
#y=7(x-9/14)^2-32color(blue)(+(-81/28))#..........................(2_a)
#y=7(x-9/14)^2-977/28#
#("So " x_("vertex")=(-1)xx(-9/14)color(white)(..)=+9/14)#
