Hey, I was wondering how do you factor (a^2-x^2)? (a squared minus x squared) or how you would go about graphing it? Thanks!
The factors are (a+x)(a-x).
To graph it, just pick a series of x values (try x = -10 to 10 in steps of one of two), calculate the corresponding values of a^2 - x^2, call those the y values, and then make a graph of the series of (x,y) values you have calculated. We cannot do the graphing for you.
You will have to choose a value of a before making the calculations and drawing the graph.
Since y = a^2 - x^2, = (a-x)(a+x),
y/a = (1 - x/a)(1 + x/a)
You could make a universal graph y/a vs x/a, and not have to choose a value of a.
I really do not understand what you mean by picking a series of x values from -10 to 10? Do you mean the window? And how do you calculate the corresponding values of a^2-x^2? And do you mean that I'm supposed to just type in a^2-x^2 into my graphing calculator because when I do that no graph shows up?
Try using graph paper instead of a calculator. If you pick value of x and a, surely you can calculate a^2 - x^2. A series of x values from -10 to 10 could be -10, -8, -6, -4, -2, 0, 2, ... 10.
If this makes no sense to you at all, consider hiring a private tutor.
You need to go through a graphing tutorial.
The following half hour tutorial is basic operations, very good:
(Broken Link Removed)
Here is a more advanced tutorial:
http://mtl.math.uiuc.edu/non-credit/basic84plus/ti84plus-tutorial/ti84-tutorial.toc.html
I made a mistake in one formula, which should be
y/a^2 = (1 - x/a)(1 + x/a)
You could either make your plot in terms of y/a^2 vs 1/x, or you would have to pick a value of a (such as 1) before making the graph, and plot y vs x.
I also made a mistake in the phrase that should have read "in steps of one OR two"
Sorry about the confusion these errors of mine may have caused.
I heartily recommend a visit to the tutorials suggested by BobPursley.
I have never used a graphing calculalor. I prefer the old fashioned way of hand drawing them, or plotting graphs from tables made by a spreadsheet such as Excel.
Okay, I totally understand now. Thanks. Sorry, I thought you were trying to explain something to me on the graphing calculator. No wonder!
To factor the expression (a^2 - x^2), you can use the difference of squares formula. The difference of squares formula states that for any two numbers a and b, the expression (a^2 - b^2) can be factored as (a - b) * (a + b).
In the case of (a^2 - x^2), you can rewrite it as (a^2 - x^2) = (a - x)(a + x). So, this is the factored form of the expression.
Now, for graphing (a^2 - x^2), you can create a table of values and plot points on a coordinate plane.
1. Choose a set of values for x. For example, you can pick -3, -2, -1, 0, 1, 2, 3.
2. Substitute each value of x into the expression (a^2 - x^2) to find the corresponding y-values.
3. Plot the points (x, y) on the graph.
4. Connect the points with a smooth curve. Since (a^2 - x^2) is a quadratic function, the graph will be a shape called a "hyperbola."
Remember to also determine the values and the behavior of the graph based on the value of a. If the value of a is positive, the graph will open upwards and downwards. If a is negative, the graph will open leftward and rightward. This will affect the shape and orientation of the hyperbola.
I hope this helps you factor and graph the expression (a^2 - x^2)! Let me know if you have any further questions.