Question

Write the equation in standard form. Determine the vertex, axis, and the direction in which the parabola opens. X2 + 4x + 2y – 2 = 0

Answer 1

The given equation is x²+ 4x + 2y – 2 = 0               or, 2y = -x²-4x+2 or, y = -x²/2 -2x +1. This is the standard form of the equation of a parabola which opens downwards ( as the coefficient of x² is negative).

The equation of the given parabola is y = - x²/2 -2x +1 = -1/2(x²+4x) +1 = -1/2(x²+2*x*2+2² ) +1+2²/2 = -1/2(x+2)² +3. This is the vertex form of the equation of the given parabola. The vertex of the parabola is the point (-2,3), it opens downwards, and the axis , being the line through the vertex, parallel; to the Y-Axis, is the line x = -2.

A graph of the parabola is attached for visual clarity.