Question

Determine the number of x-intercepts that appear on a graph of each function. f(x)= (x-6)^2(x+2)^2

Answer 1

Two x-intercepts x = -2 and x = 6

Explanation:

`f(x)=(x-6)^2(x+2)^2\to y=(x-6)^2(x+2)^2`

x-intercepts are for y = 0.

Put y = 0 to the equation:

`(x-6)^2(x+2)^2=0\iff(x-6)^2=0\ \vee\ (x+2)^2=0\\\\(x-6)^2=0\iff x-6=0\qquad\text{add 6 to both sides}\\\\x=6\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\x=-2`

Answer 2

the awnser is 2

Explanation: