Problem

Complete the square for \(x~=~y^2~+~6y~+~5\). Give the vertex and canonical forms, vertex, \(p\)-value, axis, opening direction, focus, and directrix.

Answer choices

Choose your path.

Preview only

The vertex form is x = (y - 3)² - 4; equivalently, (y - 3)² = 1*(x + 4). The vertex is (-4, 3), p = 1/4, the axis is y = 3, it opens right, the focus is (-15/4, 3), and the directrix is x = -17/4.

The vertex form is x = (1/4)(y + 3)² - 4; equivalently, (y + 3)² = 4*(x + 4). The vertex is (-4, -3), p = 1, the axis is y = -3, it opens right, the focus is (-3, -3), and the directrix is x = -5.

The vertex form is x = -(y + 3)² - 4; equivalently, (y + 3)² = -1*(x + 4). The vertex is (-4, -3), p = -1/4, the axis is y = -3, it opens left, the focus is (-17/4, -3), and the directrix is x = -15/4.

The vertex form is x = (y + 3)² - 4; equivalently, (y + 3)² = 1*(x + 4). The vertex is (-4, -3), p = 1/4, the axis is y = -3, it opens right, the focus is (-15/4, -3), and the directrix is x = -17/4.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Complete the square for \(x~=~y^2~+~6y~+~5\). Give the vertex and canonical forms, vertex, \(p\)-value, axis, opening direction, focus, and directrix.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.