Find Y-Axis Intersection: Solving y=(x+5)²+2 Quadratic Function

To find the intersection of the function $y = (x+5)^2 + 2$ with the y-axis, we follow these steps:

• Step 1: Identify that the intersection with the y-axis occurs when $x = 0$.
• Step 2: Substitute $x = 0$ into the equation $y = (x+5)^2 + 2$.
• Step 3: Perform the substitution and simplify: $y = (0+5)^2 + 2$.
• Step 4: Simplify further: $y = 5^2 + 2 = 25 + 2 = 27$.

Thus, the intersection point with the y-axis is $(0, 27)$.

The correct answer is option 4: $(0, 27)$.