# Gr 12 Calculus Question Help

Well there are actually two questions i need some help with, if you could provide a full solution so i cna see the step by stpe thing it would be nice.

Question 1
A quadratic function f(x) with integral coefficients has the following properties:
f(3/2) = 0, (x-2) is a factor of f(x), and f(4) = 50. Determine f(x).

Question 2
A cubic function g(x) with integral coefficients has the following properties:
g(3) = 0, G(-3/4) = 0, (x+2) is a factor of g(x), g(1) = -84. Determine g(x).

Thanks!

EnumaElish
Homework Helper
You could begin by writing out a general (generic) quadratic function, e.g. y = ax2 + bx + c and then think how you could solve for a, b and c. Does that help to get you started?

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i've written out what i've been given:

f(3/2) = 0 therefore (2x-3) is a factor of f(x),

Factors of f(x) = (2x-3) and (x-2)
f(4) = 50

i also wrote out ax^2 + bx + c as oyu suggested but not seeing a link.... :(

whati s the general form of f(x) ??
quadratics look like $f(x) = ax^2 + bx + c$
ok from taht what is f(2) ?? Using the formula for f(x) above and your given info form equations using f(3/2) and f(4) as well to solve for a, b, and c.

EnumaElish
Homework Helper
Dough, follow stunner's suggestion. For example, how would you write f(4) in terms of $f(x) = ax^2 + bx + c$?

i did that but no luck i'll give it another shot, i make mistakes osmetimes so its possible i may have done somethign wrong whihc messed everythign else up....

EnumaElish
Homework Helper
Go ahead and post here what you've done.

yay, i got the first one... on the third try after the above post, i kept makign silly errors just now... i'll let ya know how i do witht he the next one, thanks for the help :D

i dont think i got it right and it was hell of a lot of work... i might give it a shot tomorrow or later i got f(x) = -8x^3 - 50x^2 - 54x + 28

thanks tho i got one so i have teh idea now its just not makign stupid mistakes!

dry, we didnt even have to do number 3... i sitll try it agian later caus ei wanan find out how to do it!

HallsofIvy