Clarence
  • Clarence
"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..
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
asnaseer
  • asnaseer
your steps are correct so far
asnaseer
  • asnaseer
you now have 3 equations with 3 unknowns
asnaseer
  • asnaseer
solve these to find a, b and c and then calculate a+b+c

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Clarence
  • Clarence
I've tried to use row operations but was unsuccessful, is there a particular order that I should place these equations?
asnaseer
  • asnaseer
You could just use simple substitution, e.g. start by eliminating c using the last equation
Clarence
  • Clarence
I'm not quite sure I understand you, use 144a + 12b + c = -9 to eliminate c?
asnaseer
  • asnaseer
c = -9 -12b -144a from that equation now substitute this into your first equation
Clarence
  • Clarence
Oh, the a-b+c=2 equation?
asnaseer
  • asnaseer
yes :)
asnaseer
  • asnaseer
you will then be left with 2 equations in two unknowns - a and b
Clarence
  • Clarence
How does that help? I have -13b-143a=11 right now.
asnaseer
  • asnaseer
and you also have: 24a + b = 0
asnaseer
  • asnaseer
which gives you: b = -24a substitute that into: -13b-143a=11 and solve for a
anonymous
  • anonymous
ok what do you need help with, solving for a?
Clarence
  • Clarence
a would equal 2/169?
asnaseer
  • asnaseer
not quite - you must have made a simple algebraic mistake
Clarence
  • Clarence
Did you not get 312a-143a=2?
anonymous
  • anonymous
-13b-143a=11 -13(-24a) - 143 a = 11 312a - 143a = 11 169a = 11 /169 on both sides a = 11/169
asnaseer
  • asnaseer
remember the negative sign
anonymous
  • anonymous
me? It went away
asnaseer
  • asnaseer
I am talking to @Clarence
anonymous
  • anonymous
ok sorry just trying to help
Clarence
  • Clarence
So b = - 264/169?
asnaseer
  • asnaseer
yes :)
anonymous
  • anonymous
good job!!
asnaseer
  • asnaseer
now you are just left with c to calculate and then you can work out what a+b+c equals
Clarence
  • Clarence
c being 63/169?
asnaseer
  • asnaseer
yup :)
anonymous
  • anonymous
wow sounds like you got it down, now just add them together
Clarence
  • Clarence
So all together it'd be -190/169?
asnaseer
  • asnaseer
yes - well done! :)
anonymous
  • anonymous
correct awesome job
Clarence
  • Clarence
Oh I get it now, thanks!
asnaseer
  • asnaseer
why do I feel like there is an echo in here :)
Clarence
  • Clarence
Probably because there is ;) Thanks again guys/girls!
anonymous
  • anonymous
haha you keep typing and replying right before i do and i don't see it sorry
Clarence
  • Clarence
Aha, all good :)

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