Question

Given the function f(x) = 2(x - 1)^2 + 1, indicate the shifts that will effect the location of the vertex. What effect will they have?

f(x+3)
f(x) + 3
f(3x)
3*f(x)

Please help.. OMG. .-.

Answer 1

is the multiple choice related to this question?

Answer 2

It's part of the question, I guess. I honestly have no idea. It's an essay question, yet, it has those.

Answer 3

do you recgonize the vertex from below?
y = a(x-h)^2 + k

Answer 4

No, I honestly don't. .-.

Answer 5

thats ok,
but you do see how the vertex form is similar to the equation you give?

Answer 6

Yes, I do. They're pretty much the same.

Answer 7

so what would h equal and what would k equal looking at the two forms?

Answer 8

k would be + 1 and h - 1?

Answer 9

f(x) = 2(x - 1)^2 + 1
compare it to the general vertex form: y = a(x-h)^2 + k where (h,k) is the vertex.
You will notice h = 1, k = 1. So the original function has vertex at (1,1)

I will do the first one and you follow similar procedure for the others.
f(x) = 2(x - 1)^2 + 1
f(x+3) = 2(x + 3 - 1)^2 + 1
= 2(x + 2)^2 + 1
Compare this to y = a(x-h)^2 + k and you will see h = -2 and y = 1.
The new vertex is (-2,1). Compare it to the original vertex at (1,1) and you can see the vertex has been shifted to the left by 3 units.

You can try the rest.

Answer 10

k=1 and h=1,
these two numbers are the x and y value of the vertext of the parabola.
so it means the vertex of the parabola will be 1 to the right and 1 up from the orgin.

Answer 11

@ranga thanks for the rest of the steps!

Answer 12

no problem. I hope original poster can solve the rest.

Answer 13

Oh, Jiminy Cricket.. How did you get -2??

Answer 14

2(x + 2)^2 + 1 = 2(x - (-2))^2 + 1
compare it to: y = a(x-h)^2 + k h = -2, k = 1

Answer 15

OHHH I see! Because h in the formula is negative, whatever number in it's spot is turned to negative as well?

Answer 16

The general form has (x - h) and not (x + h) and so if we see x + 2 we will have to rewrite it as x - (-2) so we can compare it directly to x -h and say h = -2

Answer 17

Oh, okay, I get that. Now, I have no idea how to set up the others. Can you help me with them, too? I'm absolutely awful at Algebra. Hard to believe I made it to 12th grade with how bad I am.

Answer 18

answering two other questions and I will stop by in between.

Answer 19

Okay, I'll wait. I'm pretty patient. ^^;;;

Answer 20

f(x) = 2(x - 1)^2 + 1
f(x) + 3 = 2(x - 1)^2 + 1 + 3
= 2(x - 1)^2 + 4
Compare this to y = a(x-h)^2 + k and you will see h = 1 and y = 4

Originally the vertex was (1,1) and now it is (1,4)
So the vertex has been shifted up along the y axis by 3.

You should try the third part. Just replace x by 3x in the original function and simplify.

Answer 21

f(3x) = 2(3x - 1)^2 + 1
Did I set that up right?

Answer 22

Yes. Remember we keep comparing the function to y = a(x-h)^2 + k to find the vertex.
f(3x) = 2(3x - 1)^2 + 1
Inside the parenthesis we have (3x-1) but in the general function we have (x-h)
So we have to get rid of the 3 in front of x.
Factor the 3 out.

2(3x - 1)^2 + 1 =
2 { 3(x -1/3) }^2 + 1 =
2 * 3^2 * (x-1/3)^2 + 1 =
18(x-1/3)^2 + 1

Compare this to y = a(x-h)^2 + k and you will see h = 1/3 and y = 1
Originally the vertex was (1,1) and now it is (1/3,1)
So the vertex was shrunk to a third when we go from f(x) to f(3x).

Answer 23

for f(x+3) , the vertex will shift 3 units to the left
for f(x)+3 , the vertex will shift 3 units up
for f(3x) , the vertex will shift 2/3 units to the left
3*f(x) , the vertex will shift 2 units up

Answer 24

Give the last one a try yourself.

Answer 25

3*f(x)? I have no idea, but I'll give it a shot.
3*f(x) = 2(3 * x - 1)^2 + 1
Did I set that up right?? It doesn't look right. If you tell me how to set it up, I'll try it out on my own.

Answer 26

3 * f(x) means 3 * { 2(3x - 1)^2 + 1 } = 6(3x-1)^2 + 3
Vertex is (1,3). Compare it to (1,1) and the vertex has shifted up by 2 units.

BTW, for part c) say the vertex shifts 2/3 units to the left instead of saying shrunk to a third when we go from f(x) to f(3x).

Answer 27

OHHH, okay! So the 3 before the f in 3*f(x) is supposed to be multiplied tot he first number outside the brackets? Ah, I think I get it!

Answer 28

Thank you for your help!!

Answer 29

you are welcome. You can also try the shortcut method that @mangorox used but it would require memorizing a few things. Here the substitutions were fairly simple and we could see how the vertex shifted each time we shifted the original function.