The shifting of h in vertex form

[miller1991]

The Role of H in the quadratic function ( vertex form)

i get that this is how its written on a graph y=(x-2)^2+k
that the graph looks as if the value of h is positive as in +2 ( however its value is actually negative)
looks like it shifted right my textbook contradicts itself

y=3(x-1)^2 +2 or y=3(x-(-1))^2 +2

a positive ie x minus a negative ie -1 equals a positive ( thus h is positive and shifts right

the value of h is +1 thus there is a right shift 1 unit
( two positives make a negative, or subtracting a negative from a positive gives a positive )
for the example
y=-1(x-3)^2

i need to know if the value of a affects the value of h

y=-1(x-(-3))^2

if a is -1

we looking at
(x-(-3))^2 gives a positive h value
( two positives make a negative, or subtracting a negative from a positive gives a positive )

then its basically

-1(3) equals a negative ( as in a negative times a positive equals a negative) thus switches h to a negative vaule

h is -3 the function shifts left
and on the graph reads as -1(x+3)^2 or w.e (not sure if that part is right)

in short a good place for me to start is understanding if A in vertex form affects the value of H in regards to the shift of h i just need to know how to solve for the value of h
like
if the question is describe the shifting of h in this function
what does h do

and does a affect the value of h

textbook question
state the value of h and describe the shifting of the function

y=3(x-1)^2 +2
answer given H = 1 and shifts right 1 unity=-(x-3)^2
answer given
h= -3 and shifts left 3 units

as far as this book indicates a is affecting the h movement THANKS GUYS ! FOR HELPING ME GET further with this
w.e info you have to help me move forward would be appreciated.so is it possible that a does not affect the shifting of h
and these
(x-(-3))^2
invisible brackets actually mean multiplication and i am not adding and subtracting here to find the value of h

 

[topsquark]

y=3(x-1)^2 +2 or y=3(x-(-1))^2 +2

The book really doesn't contradict itself. It's that the second equation above is not the same as the first. It's merely a typo (albeit a very confusing one.) The second equation should be \(\displaystyle y = 3( x - (+1) )^2 + 2\). I don't know why they bothered with that.

I didn't spot any other problems except for this one.

-Dan

Addendum: You used H and h to represent a horizontal translation. Mathematics is case sensitive so H and h aren't the same. h is the usual symbol.