Final answer:
The vertex of the parabola x = -y² + 8y - 17 is (4, -1).
Step-by-step explanation:
The equation x = -y² + 8y - 17 represents a parabola. To find the vertex of the parabola, we need to rewrite the equation in the standard form y = ax² + bx + c. In this case, a = -1, b = 8, and c = -17.
The x-coordinate of the vertex can be found using the formula x = -b / (2a). Substituting the values, we get x = -8 / (2 * -1) = 4.
Now, we can substitute the value of x back into the equation to find the y-coordinate of the vertex. Plugging in x = 4, we get y = -(4)² + 8(4) - 17 = -16 + 32 - 17 = -1.
Therefore, the vertex of the parabola is (4, -1).