Question

HELP PLEASE! WILL FAN AND GIVE MEDAL
The function f(x) = −x2 + 48x − 432 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games sold and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem?
Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

Answer 1

so how do u find x intercepts?

Answer 2

x intercepts occur where y = 0

Answer 3

so put f(x) = 0 into ur equation and solve for x first

Answer 4

its easier if u factorise the equation first tho

Answer 5

I'm not 100% sure on how to factorise it completely

Answer 6

all good:
-x^2 + 48x -432
so what 2 numbers multiply to give 432... but adds to give 48?
factors of 432 = 1,432, 2,216, 3,144, 4,108 6,72 8,54 9,48 12,36 16,27 18,24

so which 2 add to give 48
answer = 12 and 36

Answer 7

-x^2 + 48x -432
f(x) = ( -x +36 )( x - 12)

Answer 8

FOIL that:
( -x +36 )( x - 12)
( -x^2 +36x + 12x -432)

Answer 9

so, can you solve x intercepts?:
f(x) = −x2 + 48x − 432
x intercepts are when f(x) = 0
0 = −x2 + 48x − 432
0 = ( -x +36 )( x - 12)

therefore x = ??? or x = ???

Answer 10

I think I'm overthinking it xD

Answer 11

I got some crazy numbers

Answer 12

@pooja195

Answer 13

ok... well what about this: have u ever heard of the Quadratic Formula?

Answer 14

Yes, but I haven't learned anything about it

Answer 15

u can use this on a calculator or write out shorthand and solve urself using the values from ur equation
in ur case: ur equation is:
y = ax^2 + bx + c
so a = -1
b = 48
c = -432
plug in and solve

Answer 16

12

Answer 17

Right?

Answer 18

or, easier:
0 = ( -x +36 )( x - 12)
therefore either
0 = -x +36
or
0 = x - 12
... yep, so one value is x = 12
so the other x value must be

Answer 19

36

Answer 20

perfect!
so... the hard part... what does that mean?