Question

find the vertex, axis of symmetry, x - intercepts, y - intercept, focus, and directrix for the parabola ( x = y^{2}-y - 2 ). sketch the graph.
the vertex is ( left(-\frac{9}{4},\frac{1}{2}
ight) ).
(simplify your answer. type an ordered pair.)
the axis of symmetry is ( y=\frac{1}{2} ).
(simplify your answer. type an equation.)
find the x - intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.
○ a. the x - intercept(s) is/are
(simplify your answer. type an ordered pair. type an exact answer, using radicals as needed. use a comma to separate answers as needed.)
○ b. there are no x - intercepts.

Explanation:

Step1: Find x - intercepts

For x - intercepts, set \(y = 0\) in the equation \(x=y^{2}-y - 2\).
Substitute \(y = 0\) into the equation: \(x=0^{2}-0 - 2=-2\).

Answer:

A. The x - intercept(s) is/are \((-2,0)\)