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Am i right?

  • #1
can you quickly see if i'm right, because im not positive ive done it correctly...

thnx

Homework Statement



The equation of a curve is [tex]y=f(x)[/tex], where [tex]f(x) = x^2 - 6x + 14[/tex].

Find the coordinates of the minimum point , [tex]M[/tex], of the curve

Homework Equations





The Attempt at a Solution



I completed the square to get

[tex]y=(x-3)^2 + 5[/tex]

then i used my knowledge of transformation of function to work out the answer is [tex](3,5)[/tex]

however, im not sure i did it right, im pretty sure the y-coordinate is right, but the x-coordinate may be wrong...

can you help?
 

Answers and Replies

  • #2
2,063
2
You are right.
 
  • #3
yay! thnx buddy :D
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,808
933
Look at the reasoning: if x= 3, then obviously y= (3-3)2+ 5= 0+ 5= 5. If x is any number other than 3, (x-3)2 is positive so (x-3)2+ 5 is larger than 5.
 
  • #5
o rite thnx for that, i never realised why it worked out the way it did :D

cheers lol

i just went on my transformation of function graph knowledge without understanding it hehe, silly teachers
 

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