Find Increasing Intervals for the Quadratic Function y = (x-6)(x+6)

First, we need to express the given function in a form that's easy to differentiate:

The original function is $y = (x-6)(x+6)$. Expanding this, we have:

$y = x^2 - 36$.

Next, we'll find the derivative of this quadratic function to determine the intervals where the function is increasing. The derivative will provide the slope of the tangent at any point on the function:

The derivative of $y = x^2 - 36$ is:

$y' = 2x$.

Now, we determine where the derivative $2x$ is positive. A function is increasing where its derivative is positive:

Solve $2x > 0$:

$x > 0$.

This shows that the function is increasing on the interval where $x > 0$.

Therefore, the solution to the problem is that the function is increasing for $x > 0$.