Question #7c401

1 Answer
Aug 3, 2016

The vertex is at #"(-1,2)"#.

Explanation:

The vertex of a parabola is the midpoint between the focus and the point where the axis (the axis = the line perpendicular to the directrix, and pasding through the focus), intersects the directrix.

1) Focus = #color(blue)("(-2,1)")#

2) Axis = perpendicular to the directrix through the focus: the directrix has slope #-1# so the perpendicular line has slope #+1# (product of slopes of perpendicular lines = #-1#). The line with slope #+1# through #color(blue)("(-2,1)")# is #color(red)(y=x+3)#.

3) Intersection of the axis with the dierctrix:

#color(red)(y=x+3)#
#x+y=3#

Thus the intersection is at #color(green)("(0,3)")#.

4) Midpoint between the focus #color(blue)("(-2,1)")# and #color(green)("(0,3)")# is

#"(-1,2)"#.