Find Y-Intercept of (x-7)²-40: Quadratic Function Analysis

To find the intersection of the function $y = (x - 7)^2 - 40$ with the $y$-axis, we set $x = 0$ since this is the defining property of the $y$-axis.

Substitute $x = 0$ into the function:

• Compute $y = (0 - 7)^2 - 40$.
• Calculate $y = (-7)^2 - 40$.
• This simplifies to $y = 49 - 40$.
• Thus, $y = 9$.

The point of intersection on the $y$-axis is therefore $(0, 9)$.

Therefore, the solution to the problem is $(0, 9)$.