The shifting of h in vertex form

• MHB
• miller1991
In summary: H is something else.In summary, the conversation discusses the role of h, the horizontal shift, in the quadratic function in vertex form. It is noted that while the textbook may seem contradictory, the second equation is simply a typo and should be read as y = 3( x - (+1) )^2 + 2. The conversation also considers the effect of the value of a on the value of h and the shifting of the function. It is concluded that a does affect the shifting of h, and that the invisible brackets in equations such as (x-(-3))^2 indicate multiplication rather than addition or subtraction. Ultimately, the conversation is seeking to understand how to solve for the value of h in this type of function
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
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

Last edited:
miller1991 said:
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.

1. What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.

2. How does the value of h affect the graph of a quadratic equation in vertex form?

The value of h in the vertex form of a quadratic equation determines the horizontal shift of the parabola. A positive value of h shifts the parabola to the right, while a negative value shifts it to the left.

3. What does the value of k represent in the vertex form of a quadratic equation?

The value of k in the vertex form of a quadratic equation represents the vertical shift of the parabola. A positive value of k shifts the parabola upwards, while a negative value shifts it downwards.

4. How can I determine the vertex of a quadratic equation in vertex form?

The vertex of a quadratic equation in vertex form can be determined by looking at the values of h and k. The coordinates of the vertex will be (h, k).

5. Can the value of h be equal to 0 in the vertex form of a quadratic equation?

Yes, the value of h can be equal to 0 in the vertex form of a quadratic equation. This means that there is no horizontal shift and the parabola will open either to the left or to the right depending on the value of a.

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