SOLUTION: The question I have is "Describe how the graph of f(x)=-1/4(x-5)^2 is related to the graph of f(x)=x^2." I don't need the answer, I have that! I have a math final tomorrow a

Algebra ->  Graphs -> SOLUTION: The question I have is "Describe how the graph of f(x)=-1/4(x-5)^2 is related to the graph of f(x)=x^2." I don't need the answer, I have that! I have a math final tomorrow a      Log On


   

Question 1037991: The question I have is "Describe how the graph of f(x)=-1/4(x-5)^2 is related to the graph of f(x)=x^2."
I don't need the answer, I have that!
I have a math final tomorrow and this just a study guide question.
I need to know HOW my teacher got "curves down,wider,shifts 5 units right." Thank you!
Found 3 solutions by josgarithmetic, jim_thompson5910, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You are hopefully familiar with the parabola shape y=x^2.

Adding or subtracting to the variable moves the graph left or right, that number of units. %28x-5%29%5E2 is movement five units to the right.

%281%2F4%29%28x-5%29%5E2 cuts the size of each function value by factor of 1%2F4. For example, the value which WAS 16 in x%5E2 becomes (1/4)*16=4 when you have the function as %281%2F4%29%28x-5%29%5E2.

The negative coefficient instead of the positive coefficient reflects the graph through the x-axis. -%281%2F4%29%28x-5%29%5E2 makes what was positive become negative, and what was negative become positive. Notice that %281%2F4%29%28x-5%29%5E2 has no negative values; but -%281%2F4%29%28x-5%29%5E2 will have NO positive values - only negative values and 0.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The graph of y = x^2 is a bowl-shaped graph that opens upward. Ie, the bowl is in a position where you can fill it with water and not have it spill over.

If we stick a negative in front, then the bowl turns upside down. If there was water in it, it would all come out and onto the ground. You can think of the negative as a bad thing which causes a frown shape of the graph. Whereas the original graph is a happy smile (positive coefficient ---> happy graph)


So that's what your teacher means by "curves down". Some books will say "opens downward" and it means the same thing

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The 1/4 indicates that the graph will be wider than normal. It will be horizontally pulled apart more compared to the parent graph.The reason being is that 1/4 = 0.25 is smaller than 1. Whenever the leading term outside like that is smaller than 1, the graph will be stretched in a horizontal direction.

If the term outside is larger than 1, then that means we have a horizontal compression (which leads to vertical stretching).

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The "x-5" portion shifts the graph 5 units to the right.

If you had x+5, then it would shift 5 units to the left

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There are no other transformations applied (like vertical shifting).
Here is what the parent graph looks like (green)
and what the transformed graph looks like (blue)


Graph of y = x^2 in green

Graph of y = -1/4(x-5)^2 in blue

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Heres the plot of just +f%28x%29+=+%28+x-5+%29%5E2+
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+%28+x-5+%29%5E2+%29+
Here's the plot of +-%28+x-5+%29%5E2+
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-%28+x-5+%29%5E2+%29+
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Now you are going to multiply the right side
( which is +f%28x%29+ ), by +1%2F4+. Every +f%28x%29+
that you had before will be smaller because +1%2F4+
is less than +1+. The +f%28x%29+=+0+ point is anchored
in place, so the whole parabola is not shifted down, it
has to get wider. Here's the plot of +f%28x%29+=+-%281%2F4%29%2A%28+x-5+%29%5E2+
+graph%28+400%2C+400%2C+-15%2C+15%2C+-15%2C+15%2C+-%281%2F4%29%2A%28+x-5+%29%5E2+%29+
Here's what happens by multiplying by +4+ isnstead
of +1%2F4+
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-4%2A%28+x-5+%29%5E2+%29+
Hope this helps. You have to either memorize what effect
things have, or figure it out. Figuring out works much better.