"Assume that the graph of the polynomial p(x)=ax2+bx+cpasses through the point (−1,2)and has a horizontal tangent at (12,−9). Find the sum a+b+c."
I've already substitute (-1, 2) into the polynomial equation to get a - b + c = 2 and differentiate the original polynomial to get 2ax+b=0 and replaced x with 12 to get 24a + b = 0 as well as utilizing (12, -9) to get 144a + 12 b + c = -9 but I have no idea where to go from there..

- Clarence

- chestercat

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- asnaseer

your steps are correct so far

- asnaseer

you now have 3 equations with 3 unknowns

- asnaseer

solve these to find a, b and c and then calculate a+b+c

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## More answers

- Clarence

I've tried to use row operations but was unsuccessful, is there a particular order that I should place these equations?

- asnaseer

You could just use simple substitution, e.g. start by eliminating c using the last equation

- Clarence

I'm not quite sure I understand you, use 144a + 12b + c = -9 to eliminate c?

- asnaseer

c = -9 -12b -144a from that equation
now substitute this into your first equation

- Clarence

Oh, the a-b+c=2 equation?

- asnaseer

yes :)

- asnaseer

you will then be left with 2 equations in two unknowns - a and b

- Clarence

How does that help? I have -13b-143a=11 right now.

- asnaseer

and you also have:
24a + b = 0

- asnaseer

which gives you: b = -24a
substitute that into: -13b-143a=11 and solve for a

- anonymous

ok what do you need help with, solving for a?

- Clarence

a would equal 2/169?

- asnaseer

not quite - you must have made a simple algebraic mistake

- Clarence

Did you not get 312a-143a=2?

- anonymous

-13b-143a=11
-13(-24a) - 143 a = 11
312a - 143a = 11
169a = 11
/169 on both sides
a = 11/169

- asnaseer

remember the negative sign

- anonymous

me? It went away

- asnaseer

I am talking to @Clarence

- anonymous

ok sorry just trying to help

- Clarence

So b = - 264/169?

- asnaseer

yes :)

- anonymous

good job!!

- asnaseer

now you are just left with c to calculate and then you can work out what a+b+c equals

- Clarence

c being 63/169?

- asnaseer

yup :)

- anonymous

wow sounds like you got it down, now just add them together

- Clarence

So all together it'd be -190/169?

- asnaseer

yes - well done! :)

- anonymous

correct awesome job

- Clarence

Oh I get it now, thanks!

- asnaseer

why do I feel like there is an echo in here :)

- Clarence

Probably because there is ;) Thanks again guys/girls!

- anonymous

haha you keep typing and replying right before i do and i don't see it sorry

- Clarence

Aha, all good :)

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