# Am i right?

1. Mar 23, 2007

### Trail_Builder

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

thnx

1. The problem statement, all variables and given/known data

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

Find the coordinates of the minimum point , $$M$$, of the curve

2. Relevant equations

3. The attempt at a solution

I completed the square to get

$$y=(x-3)^2 + 5$$

then i used my knowledge of transformation of function to work out the answer is $$(3,5)$$

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?

2. Mar 23, 2007

### neutrino

You are right.

3. Mar 23, 2007

### Trail_Builder

yay! thnx buddy :D

4. Mar 23, 2007

### HallsofIvy

Staff Emeritus
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. Mar 23, 2007

### Trail_Builder

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