How to plot (x^2-5)^2+y^2=16 without a calculator?

In summary, the conversation discusses the development of a pencil and paper as more efficient tools compared to the stylus and wax tablet or clay tablet. The use of pencil and graph paper is also mentioned as a way to create graphs of functions, with alternative options such as using a calculator or a computer program. The conversation ends with a reminder to show effort in solving the problem at hand.
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GravitySK
5
1
How do you think?
 
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There's this cool device called a pencil that was developed a few years ago and this ancient invention I think it was called paper with horizontal and vertical lines.

These two devices worked much better than the stylus and wax tablet or clay tablet that had to be dried out to preserve it.

I remember using pencil and graph paper worked well to create graphs of functions. First by computing a table of x,y value pairs using the function.

Alternatively, you could try:

https://www.desmos.com/calculator

Or, you could use freemat installed on your pc:

http://freemat.sourceforge.net/

Matlab:
x=[1:10]
y x.*x
plot(x,y)

LASTLY, your post looks like homework. We require you to show some effort in solving it.

Closing this thread.
 
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1. How do I plot the graph of (x^2-5)^2+y^2=16 without a calculator?

To plot this graph without a calculator, you will need to use basic algebraic principles and graphing techniques. First, rearrange the equation to solve for y. This will give you two equations, one for the positive square root and one for the negative square root. Then, choose a range of values for x and plug them into the equations to get corresponding values for y. Plot these points on a graph and connect them to create the graph of the equation.

2. Can I use a graphing calculator to plot this equation?

Yes, you can use a graphing calculator to plot this equation. However, if you want to plot it without a calculator, you will need to use basic algebraic principles and graphing techniques as mentioned in the previous answer.

3. What are the key points I should plot on the graph?

The key points to plot on the graph are the x-intercepts, y-intercepts, and any other points that satisfy the equation. To find the x-intercepts, set y=0 and solve for x. To find the y-intercepts, set x=0 and solve for y. You can also choose a range of values for x and plug them into the equation to get corresponding values for y.

4. How can I check if my graph is accurate?

To check if your graph is accurate, you can plug in different values for x and y into the equation and see if they satisfy the equation. You can also use a graphing calculator to compare your graph with the one generated by the calculator.

5. Are there any other techniques I can use to plot this equation without a calculator?

Yes, there are other techniques you can use to plot this equation without a calculator. For example, you can use symmetry to plot one half of the graph and then reflect it across the y-axis to get the full graph. You can also use transformations, such as shifting and scaling, to plot the graph.

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