Expert: Bobby Soltani - 1/6/2005

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Hi Bobby could you please answer this question
Thanks. I'm studying algebra on my own so I dont have a teacher to help me.

Graph the parabolas in the same coordinate plane and then compare their graphs.

y=x^2, y=1/2x^2 and y=4x^2

(I usind ^2 for squared)


thanks a lot Bobby.
Answer -
Hi Nelly,

I can't really help with the graph because I only have access to this text box.  To graph these parobolas, start at x = 0 and move to the right.  For the first problem
x = 0, y = x^2 = 0
x = 1, y = 1
x = 2, y = 4
etc...

Then draw the same thing on the left side of the y-axis.  When you are finished with all three graphs, the 1/2x^2 should be a very wide bowl shape, the 4x^2 will be a narrow bowl shape, and the x^2 graph will be in the middle.  I hope this helps you.

Bobby


Well Bobby my book doensnt explain on details that why I dont understand
this is on my book

x     y        (x,y)
_________________________
0     0        (0,0) I know that this comes from x and Y
1     1        (1,1)
2     4        (2,4)
3     9        (3,9)
-1    1        (-1,1)
-2    4        (-2,4)
-3    9        (-3,9)


how can get de result for x and y can I continue with 4  16 how i get -1 1 and
-2 4 etc.

Thanks again Bobby.

Answer -
Hi,

For any x value, you can plug it into the equation to get y.  For instance, x = -3, then
y = (-3)^2 = 9

x=5
y = 5^2 = 25

x = -6
y = (-6)^2 = 36

for the equation y=4x^2, you would have

let x = -3
then y = 4*(-3)^2 = 4*9 = 36

I hope that helps.

Bobby

sorry Bobby to bother u with my questions

yes i know that part where u could substitude any number but to get y=x^2, y=3x^2, and y=-2x^2 would u substitude the same number for all of them


Answer -
I'm sorry.  I'm not really sure what you asking.  Go to this website where you can see what the graph of these functions should look like.

http://www.walterzorn.com/grapher/grapher_e.htm

Copy and Paste the following in the box under the Function f(x) and click on the "plot graph" button.

x^2; 1/2*x^2; 4*x^2

Bobby



sorry Bobby that i didnt explain to U what it really my question was about. THANKS VERY MUCH FOR U REPLYS.

OK HERE IS AGAIN:

To graph a parabola
1. how can i chose the number of the variable x I pick the numbers on my own, or is there a way to do it? I want to do it without a calculator. please can you help me, I appreciate.

on my book is this equation but doesnt explain how to do it step by step.
the only step that i know is ones i have the numbers on the variable x i know how to do it for the variable y. but were i can get the number for tha variable x?

Y=x^2
x     y        (x,y)
_________________________
0     0        (0,0) I know that this comes from x and Y
1     1        (1,1)
2     4        (2,4)
3     9        (3,9)
-1    1        (-1,1)
-2    4        (-2,4)
-3    9        (-3,9)


2. Do I going to use the same numbers of the variable x as on equation y=x^2 for these other 2 equations? 1/2*x^2; 4*x^2 or for any equation?

Thanks a lo Bobby!


Answer
Hi Nelly,

You can use any x you choose and get a corresponding y value.  For instance, if you want to graph the equation from x=-10 to x = 10, you would solve for y using x = -10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9, and 10.  Then, you will have several x,y pairs that you can plot on a graph.  For the other two equations, you can use the same x values and plug them into the equations to get the new y values.

For a simple example, let's say I want to plot the three equations from x = -2 to x = 2.  For the first equation, we have,
x = -2, y = (-2)^2 = 4
x = -1, y = 1
x = 0, y = 0
x = 1, y = 1
x = 2, y = 4
Now, we can plot these points on a graph that has x on the horizontal axis and y on the vertical axis.  For the second equation,
x = -2, y = 1/2*(-2)^2 = 2
x = -1, y = 1/2
x = 0, y = 0
x = 1, y = 1/2
x = 2, y = 2
Now, we can plot this on the same graph.  Do the same thing for the third equation.  If you want more points, solve for y at more x values.

Let me know if you have questions.

Bobby