Question

What is the vertex of the parabola x = −y² + 8y − 17?

A) (4, 9)
B) (8, 4)
C) (9, 4)
D) (17, 8)

Answer 1

The vertex of the parabola x = -y² + 8y - 17 is (4, 13).

Step-by-step explanation:

The given equation is x = -y² + 8y - 17.

To find the vertex of the parabola, we need to rewrite the equation in the form y = ax² + bx + c.

Rearranging the given equation, we get y² - 8y + x - 17 = 0.

The coefficients of this quadratic equation are a = 1, b = -8, and c = (1-17) = -16.

The x-coordinate of the vertex can be found using the formula x = -b/2a. Plugging in the values, we get x = -(-8)/(2*1) = 4.

Substituting this x-value into the equation, we get y = 4 – 8 + 17 = 13.

Therefore, the vertex of the parabola is (4, 13).

Answer 2

The vertex of the parabola x = -y² + 8y - 17 is (9, 4).

Step-by-step explanation:

The given equation is x = -y² + 8y - 17. To find the vertex of the parabola, we need to rewrite the equation in the standard form of a parabola, which is y = ax² + bx + c.

Let's rearrange the equation and complete the square. x = -y² + 8y - 17 can be rewritten as y² - 8y + x + 17 = 0.

Now, let's complete the square. After completing the square, the equation becomes (y - 4)² = -x + 1. The vertex form of the equation is (y - k)² = 4a(x - h). Comparing the two equations, we can conclude that the vertex of the parabola x = -y² + 8y - 17 is (1, 4). Therefore, answer option C) (9, 4) is the correct vertex.