Question

If f(x) = ax^2 - 12x + c and f(-3/2) = 8 is the maximum value, find the values of a and c.

Answer 1

it has to do something with mentioning my name... since the username contain *** signs the question goes numb when someone mentions my name :/

anyway where was u ?
did u make it a complete square ?

Answer 2

Erm.

f(x) = ax^2 - 12x + c

f(-3/2) = 8 but f(-3/2) also equals a(-3/2)^2 - 12(-3/2) + c. Also note that the x-coordinate at the max value is -b/2a. Good luck!

Answer 3

y = ax^2 -12x + c
= a [ x^2 - (12/a)x + c/a ]
= a [ ( x -6/a )^2 + c/a - 36/a^2 ]
= a [ ( x-6/a)^2 + (ac -36)/a^2 ]
= a ( x - 6/a)^2 + (ac - 36)a

did u make it this far... ?

Answer 4

I thought that when you're completing a square, you only divide the first and second term by a?

Answer 5

-b/2a is -3/2. b is -12.

Answer 6

yes ... but u must make it a perfect square

Answer 7

when this graph takes it maximum value
a( x - 6)^2 should equal to zero
then the max value
8 will equal to (ac - 36)/a

which means
(ac -36)/a = 8
and now u have another equation ...

Answer 8

now all u have to do is solve the 2 simultaneous equations and get the values for a , c

Answer 9

the first one was
9a + 4c = -40 ------(1)
ans the second one is
8a - ac = -36 -----(2)

Answer 10

got it ?