Question

Answer the questions below about the quadratic function.

Answer 1

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

$f(x)=3x^2-18x+23\\ f(x)=3(x^2-6x)+23\\ f(x)=3(x^2-6x+9-9)+23\\ f(x)=3(x-3)^2-27+23\\ f(x)=3(x-3)^2-4$

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 $x=3$.