Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function f(x)=-3(x-4)(x-6)

The maximum value of the function is 3.

Step-by-step explanation:

Given;

f(x) = -3(x-4)(x - 6)

f(x) = -3[x² - 6x  - 4x   +  24]

f(x) = -3[x² - 10x   +  24]

f(x) = -3x² +  30x   -  72

a = -3,   b = 30,    c =  -72

For maximum point: a < 0

For minimum point: a > 0

Since a = -3, the function has maximum points

The maximum points = (x , y)

x = -b/2a

x = -30/(2 x -3)

x = -30/-6

x = 5

y = f(-b/2a) = f(5)

f(5) = -3(5)² + 30(5)  -  72

f(5) = -75  +  150  - 72

f(5) = 3

Therefore, the maximum value of the function is 3.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950