Sketch the following graphs?
Sketch the following graphs:
y=x(3-x)(2x+3)
y=x^2(x-2)(x+3)
y=(x+2)^2(3x+4)^2
I thought about perhaps finding the value of x but it doesn't seem to work.Im not sure what method I should be suing,I looked online but couldn't find any video to help me.
y=x(3-x)(2x+3)
y=x^2(x-2)(x+3)
y=(x+2)^2(3x+4)^2
I thought about perhaps finding the value of x but it doesn't seem to work.Im not sure what method I should be suing,I looked online but couldn't find any video to help me.
Original post by Dragolien
I think that your goal here is to find the points where the graphs intercept the axes. So for example, to find the roots of the first equation, make x or one of the brackets zero, and that will make y equal zero, so that would be a root of the equation.
For the first question I made x= -3 and x= -3/2
Original post by Anonymous1502
For the first question I made x= -3 and x= -3/2
The first equation is y=x(3-x)(2x+3).
x = -3/2 would be a root of the equation. This would give you -3/2(3/2)(0) which makes y = 0.
x = -3 would NOT be a root. This gives you -3(6)(-3) which equals 54. I believe that you mean 3, which would make the (3-x) bracket equal 0.
You are missing one more root. Don't forge that there is a lone x in the equation, so setting x to equal zero would also mean that y is 0. So this would be the third root.
You must also look for the y-intercept, but in this case the graph passes through the origin, so this is not necessary in this case. But this may not always be the case, so you shouldn't forget it.
Original post by Anonymous1502
For the first question I made x= -3 and x= -3/2
It should be x = 3, x = -3/2 and x = 0 (don't forget the lone x) - this is where the line intercepts the x axis.
You may also want to find the y intercept by setting x = 0.
Given there are three x intercepts, you can predict that it will generally follow the shape of an x3 graph, but you need to figure out if it's the positive or negative shape. A quick way to do this is shove in any value for x and see whether it's above or below the x axis.
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