I need help graphing an equation?

Question

Below is what my assignment is. However, I am just asking for a graph of the four equations. I am bad at graphing, but if someone can help me with a graph I can describe what I see.

Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points.

a. Y = 3X2

b. (X-1)2 + (Y-8)2 = 16

c. (X+2)2 + (Y-4)2 = 36

d. Y = X2 - X

Answer 1

I can't draw you graphs here, but I can help you become

good at graphing the equations yourself. Having graph paper

will help a lot, otherwise you'll have to draw your own X & Y

axes and mark them off using a ruler. Of course, you can

also search the internet. Go to google.com and type in

"print your own graph paper". There's plenty to choose from.

First one, y = 3x^2. Select a few values for x. Always a good

idea to choose zero among them.

Try x = -2, -1, 0, 1, 2. Work out what y should be for each x

and plot the points on the graph.

You should get the points (-2, 12), (-1, 3), (0, 0), (1,3), (2, 12).

Then draw in smooth lines between the points. It doesn't

matter if it's not exact.

If it looks as though there are going to be some critical

points, choose some more values for x to fill in the gaps.

This one is called a parabola with the concavity facing

upwards and it is symmetrical about the Y-axis. It has a

minimum point at x = 0. There are no maximum points.

With the second one, (x - 1)^2 + (y - 8)^2 = 16, it may be

best to transform it into y = 8 ± sqrt[16 - (x - 1)^2].

Notice that for each x value there are two y values.

Also note that 16 - (x - 1)^2 must be >= 0 for real y.

That is, x must be between -3 and 5, inclusive.

So try x = -3, -2, -1, 0, 1, 2, 3, 4, 5 and see what you get.

Can you find the centre point? See how it relates to the

original equation. Can you find the radius? How does it

relate to the 16 in the original equation?

Third equation is much the same as the second.

The fourth equation is similar to the first one, except that

it is shifted a little. Notice where the graph cuts the X-axis.

This happens, of course, when y = 0, that is, x^2 - x = 0.

Factorising gives x(x - 1) = 0, which gives x = 0 or 1.

Where is the minimum point? Note that because of

symmetry, the x value is exactly halfway between 0 and 1,

that is 1/2. Now plug in x = 1/2 into the equation to find out

the value of y.