Question 1209270
**1. Rewrite the Equation**

* Start by rearranging the equation to isolate 'x': 
   x = y² - 8y + 4y² - 15y + 16
   x = 3y² - 23y + 16

**2. Complete the Square**

* **Factor out the coefficient of y²:**
   x = 3(y² - (23/3)y) + 16

* **Inside the parentheses, add and subtract the square of half the coefficient of y:**
   x = 3(y² - (23/3)y + (23/6)² - (23/6)²) + 16

* **Rewrite as a perfect square trinomial:**
   x = 3[(y - 23/6)² - 529/36] + 16

* **Distribute the 3:**
   x = 3(y - 23/6)² - 529/12 + 16

* **Simplify:**
   x = 3(y - 23/6)² - 145/12

**3. Identify the Vertex**

* The equation is now in vertex form: x = a(y - k)² + h 
    * Where (h, k) represents the vertex of the parabola.

* In this case:
    * h = -145/12
    * k = 23/6

**Therefore, the vertex of the graph is (-145/12, 23/6).**