Hi Need Urgent help will be extremely grateful

Well, you have to try SOMETHING. I can see one value for x that makes y = 0, just by looking at it. Can you? If you can, then you are on your way toward finding the other three.
 
Find the values of x that make y = 0. There are 4 of them, since the equation is degree 4 in x. However, some of those four may appear more than once.

Hint: 4x^4+12x^3+9x^2 = (x^2)*(4x^2+12x+9)
 
Yeah i found out that this is meant to be a quartic. and i have to find x and y intercepts. I found 0=X^2(2x+3)(2x+3). for x intercepts
I think from there i separate into two?

x^2=0. so x= 0. , 2x+3=0 so x =-3/2.
 
Here's the things you should find:
- y-intercept
- x-intercepts
- stationary points and what sort they are
- oblique inflection points
- what happens at the ends of the graph
Do you know how to do all of those things?
 
I dont know how to find any of that. I entered the equation into a graph generator and it drew a graph with the x and y intercepts. So I factorised the equation and found two x intercepts -3/2 and 0 and i found y intercept = 0.
On the graph it shows that this is right but there is a global maximum point that I dont understand or know how to find.
 
y-intercepts are easy. Think about this: Every point on the y-axis has an x-coordinate of 0. Right? So to find the y-intercept, just plug in x=0. Try it!

x-intercepts : Every point on the x-axis has a y-coordinate of 0. Right? So put it y=0 and solve the equation.
i) y = 4x^4+12x^3+9x^2 becomes 0=4x^4+12x^3+9x^2=(x^2)*(4x^2+12x+9) as tkhunny told you. Can you take it from there?

To do the rest you need some calculus.
Have you studied any calculus?
 
StudentHelp said:
I need to Sketch the following showing all essential features:
i) y = 4x^4+12x^3+9x^2
Click to expand...
What "all essential features"means depends on what you have been taught! If you're studying calculus, it will include things like maxima and minima; if you are only in precalculus (that is, algebra), it will only go as far as intercepts and behavior there (multiplicity). Unfortunately, you didn't put the question under either calculus or algebra, but under geometry and trigonometry, neither of which is involved here. So I have no idea.

Look at examples in your textbook to see what they are asking for; or the instructions for a group of exercises may explain that. I see you mentioned "global maximum point", though that was not in the problem as you stated it; does this suggest you're not telling us some things you know, or did you get that from somewhere else?
 
Whatever is going on with this function, there is no GLOBAL maximum. As x goes to plus or minus infinity, what happens to the value of the function? There is, however, a global minimum.
 
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