Question

Answer the questions below about the quadratic function.


`f(x)=3x^2-18x+23`

(a) Does the function have a maximum or minimum value?

(b) What is the function's minimum or maximum value?

(c) Where does the minimum or maximum value occur?

Answer 1

Given the function
`f(x)=3x^2-18x+23`. The above function can be written as

`image`

a)Now, the function
`f(x)=3(x-3)^2-4` has minimum value since the coefficient of
`(x-3)^2` is
`3>0`.

b) The minimum value of the function occurs at
`x=3` and its value is

`f(3)=3(3-3)^2-4 =-4`

c)The minimum value of the function occurs at
`x=3`.