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What effect will replacing x with (x−4) have on the graph of the equation y=(x−3)2 y = ( x − 3 ) 2 ?

User Thomas Jaunism
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1 Answer

18 votes
18 votes

Answer:

y"= 2 wich is positive

Explanation:

Explanation:

Our equation is: y=(x-3)²

x should be replaced by x-4

y=(x-3)²

y=[(x-4)-3]²

y=(x-4-3)²

y=(x-7)²

The graph is still a parabola but with a different vertex

The vertex here is :

y= (x-7)²

y= x²-14x-49

y'= 2x-14

solve y'=0

2x-14=0

2x=14

x=7

You can easily find it without derivating by dividing -14 by -2

since: x²-14x-49

a=1 b= -14 c=-49

-b/2a = 14/2 = 7

the image of 7 is:

y=(7-7)² = 0

so the coordinates of the new vertex are (7,0) and it's a maximum

since y">0

y'= 2x-14

y"= 2 wich is positive

User Taymless
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