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So 16 = a(4)^2 - b4 -c
and
48 = a(10)^2 -b(10) - c

yeah Im so lost I don't even know what this means :(

do you still need help?

yes!

ok so can you tell me what the general form of a quadratic function is?

if not thats ok, i need to see what you know and what you dont

I don't

|dw:1433582094129:dw|

so like
a= 1/2
b= -2
c= 18
this is what I got so far

ok so if
a = 1/2
b = -2
and c = 18
then what would the general form look like?

1/2x^2+(-2x)+18?

perfect

and simplying you get 1/2x^2 - 2x + 18

ok good i think you are ready to set up the problem

does this make sense?

so you will input the number of widgets, x, into the function and the output will be the cost, c(x)

does all of this make sense so far?

can you set it up for me this is a little confusing

you should set it up, so that when you are taking a test, you can do it yourself

cost = c(x) = output
number of widgets = x = input

cost is the same thing as c(x)
number of widgets is the same thing as x

ok so lets start with the first example

they said the cost was 16, so can you plug the 16 into this equation?
c(x) = ax^2 + bx + c

so c(x) = 16x^2 -2x +18

no remember cost is the same thing as c(x)

if cost is 16
and cost is c(x)
what is c(x)?

16

perfect, so c(x) = 16 lets plug it in

c(x) = ax^2 + bx + c
now im plugging in c(x) = 16
16 = ax^2 + bx + c

ok yes that makes sense

good

so now remember widgets is the same thing as x, and it says it costs 16 to produce 4 widgets

so we have
16 = ax^2 + bx + c
can you plug 4 in here in the correct place?

x is the number of widgets
the number of widgets is 4
so x must be?

and what about a b and c?

dont worry about those yet

step by step

so whats our equation look like now?

16=a(4)^2 -2(4) +18?

perfect

oh actually that last one should be 16 = a(4)^2 + b(4) + c sorry

yes I thought so too

can you set up the other equatoin now?

cost is 48 to produce 10 widgets, plug the given values into the equation
c(x) = ax^2 + bx + c

48= a(10^2) -b(10) +c

very close, except its +b(10) not -b(10)

sorry I got mixed up because b is -2

ok perfect so we have these two equations:
16 = a(4)^2 + b(4) + c
48 = a(10)^2 + b(10) + c

all good

can you simplify those two equatoins?

I don't know how

ok i will do one you do the other

alright that was too easy all you did was square the 4

exactly

ok so we have these two equations:
16a + 4b + c = 16
100a + 10b + c = 48

well actually, hold on.

48= a(10^2) +b10 +c
48= a100 +b10 +c

perfect :)

nope

wait, are we missing the initial condition value?

that's only 2 equations. we have three unknowns.

ok are you still here sarah?

brb i need to grab something to eat

let me know if you are still here sarah and we can finish the problem

yes

ok great, are you familiar with solving systems of equations?

yes!

let me know the values you get for a and b

ok so what do I solve for a?

you solve the system of those 2 equations for
a
and
b

sarah please let me know what you get for the values of
a
and
b

a=-b/4+1
b=-4a+4
now the seconf one

yes what you wrote is correct, however you need to find the number value for both
a and b

are you familiar with solving systems of equations by substitution or elimination or both?

i didnt check if it was correct though

what did he say was the answer?

it was wrong... I failed.. and its 3 am im tired im just gonna cut and go to sleep ;c

fill in

problem with rounding probably...

unless they assumed a value for c or something.