Question

"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..

Answer 1

your steps are correct so far

Answer 2

you now have 3 equations with 3 unknowns

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

c = -9 -12b -144a from that equation

now substitute this into your first equation

Answer 8

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

Answer 9

yes :)

Answer 10

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

Answer 11

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

Answer 12

and you also have:

24a + b = 0

Answer 13

which gives you: b = -24a

substitute that into: -13b-143a=11 and solve for a

Answer 14

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

Answer 15

a would equal 2/169?

Answer 16

not quite - you must have made a simple algebraic mistake

Answer 17

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

Answer 18

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

Answer 19

remember the negative sign

Answer 20

me? It went away

Answer 21

I am talking to @Clarence

Answer 22

ok sorry just trying to help

Answer 23

So b = - 264/169?

Answer 24

yes :)

Answer 25

good job!!

Answer 26

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

Answer 27

c being 63/169?

Answer 28

yup :)

Answer 29

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

Answer 30

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

Answer 31

yes - well done! :)

Answer 32

correct awesome job

Answer 33

Oh I get it now, thanks!

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

Aha, all good :)