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2. Heinz has a list of possible functions. Pick one of the g(x) functions below, show how to find the zeros, and then describe to Heinz the other key features of g(x). • g(x) = x3 – x2 – 4x + 4 • g(x) = x3 + 2x2 – 9x – 18 • g(x) = x3 – 3x2 – 4x + 12 • g(x) = x3 + 2x2 – 25x – 50 • g(x) = 2x3 + 14x2 – 2x – 14
@butterflydreamer why do you keep coming here and leaving???
LOOOOL because i want to help xD BUT i'm not that great at this -.-
Haha its fine, I was just like "the heck is she doing leaving and coming?" Well do you have anyone you know who can help me?
sorrry xD I'm pretty sure the qualified helpers can help :) Firstly you should choose one of the g(x) functions to use
for the first part, when you want to find the 0's, you set g(x) = 0... then factorise and solve for x. So e.g. if you use the first one: g(x) = x^3 - x^2 - 4x + 4 \[g(x) = x^3 - x^2 -4x + 4 \rightarrow x^3 - x^2 - 4x + 4 = 0 \]
you can factorise that to get: |dw:1436366996300:dw|
@butterflydreamer so the answer is x= +-2,1
hmm yeah, but only if YOU choose to use the first equation. I'd suggest you pick a different one on your own though :)
@butterflydreamer here is the other question. 3. Provide a rough sketch of g(x). Label or identify the key features on the graph.
when you identify the zeros of a function, the values of x will be your x-values when y = 0. So basically, when g (x) = 0 , x = -2 , + 2 , 1 Note: (-2, 0) , (2, 0), (1,0) are your x-intercepts basically. looking at your relation: \[g(x) = x^3 - x^2 - 4x+ x \] Can you see that your relation is a cubic? Since the highest degree is 3. Also note how x^3 is POSITIVE and not -x^3. So it's positive curve.
Ok. So I how would I do the graph though? I will have to use a curved line correct?
so try to graph it.. knowing that it is: - a positive cubic curve - has 3 x-intercepts at ( -2, 0) , (2, 0), (1, 0) OH i forgot, also work out your y-intercept :) so when x = 0 , y= ? to do this we have : y = x^3 - x^2 - 4x + 4 so set x = 0 and we get \[y = (0)^3 - (0)^2 - 4(0) + 4 = ? \] TO SUMMARISE. To sketch a cubic: 1. identify if it is a positive/negative cubic curve (ask yourself if x^3 is + / -) 2. find x-intercepts (set y = 0) 3. find y-intercept (set x = 0) |dw:1436369493931:dw|
Ok I think I get it. Thank you so very much!!!
you're welcome :) hope it was helpful LOLLL (i tried xD)
Well I do I have one last one. Sorry! I didn't see it lol. I'll post it see if you can help me with it.
4. Esmeralda is graphing a polynomial function as a parabola. Before she begins graphing it, explain how to find the vertex. Make sure you include how to determine if it will be a maximum or minimum point. Use an example quadratic function to help you explain and provide its graph.
okaay, this question is hard for me to explain.. LOL close this question and post it as a new one :) I'm sure many other users will be able to help you :)
OK thank you lotts!!!
noo problem :D