Question

Find the vertex of the graph of the equation x - y²+8y = 13.

a) (5, 3)
b) (5, -3)
c) (-5, 3)
d) (-5, -3)

Answer 1

To find the vertex of the graph of the equation x - y² + 8y = 13, rewrite the equation in vertex form by completing the square. The vertex is then given by the coordinates (h, k) in the vertex form, which in this case are (4, -3).

Step-by-step explanation:

To find the vertex of the graph of the equation x - y² + 8y = 13, we first need to rewrite the equation in vertex form. The vertex form of a parabola is given by y = a (x - h) ² + k, where (h, k) represents the coordinates of the vertex. So, let's complete the square to rewrite the equation:

1. Add and subtract 16 to the equation to make it a perfect square trinomial: x - y² + 8y + 16 - 16 = 13 - 16.
2. Rearrange the equation and group the square terms together: (x - 4) - (y - 4) ² = -3.
3. Now, the equation is in vertex form. The vertex is given by the coordinates (h, k), which in this case are (4, -3).

So, the correct answer is (4, -3).