What is the the vertex of y=(x3)2+7x12?

1 Answer
Feb 29, 2016

Vertex(x,y)(12,314)

Explanation:

You have to combine these variables before you can do any thing else.

Given: y=(x3)2+7x12

y=x26x+9+7x12

y=x2+x3...........................(1)

From this point you can 'complete the square' or do a part version of the process.

I am opting for the part process

Write as:

Consider the coefficient of +x in equation ( 1 ), which is 1
Apply (12)×1=12

xvertex=12....... Fast isn't it!
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A word of warning: Given the standard form of
y=ax2+bx+c you need to convert this to

y=a(x2+bax)+c

In your case a=1
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute x=12 into equation (1)

yvertex=(12)2+(12)3

yvertex=14123=314
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Vertex(x,y)(12,314)

Tony B