Question

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

Answer 1

ok.. it took me a while..
from the first data
what is the equation u can get from the data f(-3/2) = 8

Answer 2

9/4a + 18 + c = 8
9a + 4c = -40

Answer 3

ok... now moving on to the second ....
they say that the maximum value of this graph is 8
which means that the vertex of this graph will be ( -3/2 , 8)
now just forget it for a while....
if a function is written as
y = ( a + b) ^2 + c
then do u know how to find the minimum point of this just by looking at it ?

Answer 4

srry
the function should be
y= (ax + b) ^2 + c

Answer 5

if the function is
y = ( ax + b)^2 + c
this will take it's minimum value when the part ( ax + b)^2 becomes zero...
which means that the minimum value of this function is c

also if the function is a maximum
y = - ( ax + b)^2 +c
this will take it maximum value when the part ( ax + b)^2 becomes zero...
which means here also the max value is c

did u get it ?

Answer 6

Yes.

Answer 7

so.. if u can
arrange
y = ax^2 -12x + c in to a format where u can write it as something like
y = -( x + q)^2 +r
what will be the value of r ?

Answer 8

got it ?