Find Y-Intercept of (x+2)²+3: Quadratic Function Analysis

To solve the problem of finding the intersection of the function $y = (x+2)^2 + 3$ with the Y-axis, we will follow these steps:

Let's begin with identifying the point where the function intersects the Y-axis. A point on the Y-axis always has $x = 0$. So, we’ll substitute this value into the function to find the corresponding y-coordinate.

Substitute $x = 0$ into the function:

$y = (0+2)^2 + 3$

First, calculate $(0+2)^2$:

$(0+2)^2 = 2^2 = 4$

Then add 3 to the result:

$y = 4 + 3 = 7$

Thus, the intersection point on the Y-axis is $(0, 7)$.

Therefore, the solution to the problem is $(0, 7)$.