SOLUTION: how do I graph y=x^3-5x+1 without using a calculator?

Question 1205524: how do I graph y=x^3-5x+1 without
using a calculator?
Found 3 solutions by ikleyn, josgarithmetic, math_tutor2020:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
how do I graph y=x^3-5x+1 without using a calculator?
~~~~~~~~~~~~~~~~~~~~~~~~

You may use your graphing calculator.

Alternatively, you may use online graphing tool at this web-site
www.desmos.com/calculator

For it, go to this web-site and print the equation of the function in the specialized window/port.

You will get your plot in the next instance, for free.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
You are learning what a degree-three polynomial function looks like? Positive lead coefficient, +1, the graph comes upward from the left, and goes upward far far to the right. Your College Algebra skills may or not be enough to identify the roots; but you can easily determine that y intercept is at 1.

In case you are learning derivatives in Calculus, you can find the local maximum and minimum points.
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The idea is to plot a bunch of (x,y) points to draw a curve through them. The more points, the more accurate the curve.

To generate any given point, plug in some value for x to find y.

Let's say we did x = 0.
y=x^3-5x+1
y=0^3-5*0+1
y=0-0+1
y=1
The point (0,1) is on this curve.

Now try x = 1
y=x^3-5x+1
y=1^3-5*1+1
y=1-5+1
y=-3
The point (1,-3) is on this curve.

Repeat the process for other x values to generate a table such as this

x y
-2 3
-1 5
0 1
1 -3
2 -1

Feel free to try other x values.

Once you have your (x,y) points, plot them on the same xy grid and draw a curve through them.

Keep in mind that I'm using technology to plot the green curve shown above. For now the only real way to know when and where the curve changes direction is to plot more points to see a more accurate version of the curve.
Later on you can use Calculus to pinpoint the local min and local max.

GeoGebra and Desmos are two of many graphing tools that you can use for verifying the answer.

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If you had a table of points such as this

x y
-2 3
-1.5 5.125
-1 5
-0.5 3.375
0 1
0.5 -1.375
1 -3
1.5 -3.125
2 -1

then the graph would be

which is a slightly more accurate look.

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