Question

Can someone help me sketch each function, showing the x-intercepts and end behavior.

f(x) = 3(x-2)2(x+5)

g(x) = -4x2(x+3)(x-1)

Answer 1

The zeros are trivial, given the complete factorizations. Think about end behaviors and find the y-intercept (x = 0). That should about do it.

Answer 2

I used the equation given and plotted it into a graph, this this give me the correct x-intercepts and end behavior?

Answer 3

f(x) = 3(x-2)2(x+5)

Cubic and positive. As x increases in the positive direction f(x) increases in the positive direction. A x increases in the negative direction, f(x) keeps increasing in the negative direction.

Two zeros at x = 2. It will have to touch the x-axis at (2,0)
One zero at x = -5. It crosses at (-5,0)
Substitute x = 0 and we see f(0) = 3(4)(5) = 60

Please do SOMETHING to indicate an exponent. Very confusing just to have a 2 floating around in there.

Answer 4

Sorry about that, it's:

f(x) = 3(x-2)^2 (x+5)

g(x) = -4x^2(x+3)(x-1)