Math Help Forum: parabolas

x = -1/2y squared - y - 4

x = -1/2y squared - y - 4

i need the vertex, x intercept, y intercepts and directrix...that would be marvelous.

Originally Posted by brittneyv

oops i forgot about that part.
sorry, i need the vertex, directrix, x-axis and y-axis.

Re-write the equation into the vertex-directrix-form:



The vertex has the coordinates

Therefore the directrix has the equation d:

With your need for x-axis and y-axis I assume that you mean the x and y intercepts of the parabola:

x-intercept: y = 0:



y-intercept: x = 0:

The LHS is negative, the RHS is a square - but a square can't be negative and therefore there doesn't exist any y-intercept.

Another attempt: The vertex is left of the y-axis and the parabola opens to left. Therefore the parabola and the y-axis can't have a common point. Thus: No y-intercept.