Question

Complete the square
to find the vertex
of this parabola.
x?+8y+2x - 23=0

Answer 1

The vertex of the parabola is;

([-1], [3])

Explanation:

The given quadratic equation is presented as follows;

x² + 8·y + 2·x - 23 = 0

The equation of the parabola in vertex form is presented as follows;

y = a·(x - h)² + k

Where;

(h, k) = The vertex of the parabola

Therefore, we have;

x² + 8·y + 2·x - 23 = 0

8·y = -x² - 2·x + 23

y = 1/8·(-x² - 2·x + 23)

y = -1/8·(x² + 2·x - 23)

y = -1/8·(x² + 2·x + 1 - 23 - 1) = -1/8·(x² + 2·x + 1 - 24)

y = -1/8·((x + 1)² - 24) = -1/8·(x + 1)² + 3

Therefore, the equation of the parabola in vertex form is y = -1/8·(x + 1)² + 3

Comparing with y = a·(x - h)² + k, we have;

a = -1/8, h = -1, and k = 3

Therefore, the vertex of the parabola, (h, k) = (-1, 3).