Verifying Coordinates of Curve Minimum Point: y=f(x) = x^2 - 6x + 14

[Trail_Builder]

can you quickly see if I'm right, because I am not positive I've done it correctly...

thnx

Homework Statement

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

Homework Equations

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

can you help?

 

[neutrino]

You are right.

 

[Trail_Builder]

yay! thnx buddy :D

 

[HallsofIvy]

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.

 

[Trail_Builder]

o rite thnx for that, i never realized 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