Question

Describe how to find what value of x must be to minimize the function f(x) = 9x^{2} - 36x + 32 using factoring.

Answer 1

Answer: x=2, f(x)=-4

Step-by-step explanation:

Given

$f(x)=9x^2-36x+32$

Solving it, add and subtract 4 to it

$\Rightarrow f(x)=9x^2-36x+36-4\\\Rightarrow f(x)=(3x)^2+(6)^2-2\times 3x\times 6-4\\\Rightarrow f(x)=(3x-6)^2-4\\\\\text{here minimum value of }\ (3x-6)^2\ \text{is 0 for x=2}\\\text{so mnimum value of }\ (3x-6)^2-4\ \text{is}\ -4$

Answer 2

Answer: after you factor use the results (3x-6)^2 - 4 to find the minimum X value but picking a number for the X value to solve to 0.

Step-by-step explanation:

Plug x=2 into the equation and it solves to 0 leave out the -4 because this is the y value