Find Y-Axis Intersection: Solving y=(x-3)²-4 Quadratic Function

Find the intersection of the function

$y=(x-3)^2-4$

With the Y

The problem asks us to find where the parabola given by $y = (x-3)^2 - 4$ intersects the y-axis. The intersection with the y-axis occurs where $x = 0$. Let's find the value of $y$ by substituting $x = 0$ into the equation:

$y = (0 - 3)^2 - 4$

Simplify inside the parentheses:

$y = (-3)^2 - 4$

Calculate $(-3)^2$:

$y = 9 - 4$

Subtract 4 from 9:

$y = 5$

Thus, the intersection of the function with the y-axis occurs at the point $(0, 5)$.

The correct answer from the choices provided is $(0,5)$.