vertex. Since the first term of the polynomial is positive, we know that the
parabola opens upward and has a minimum point at (–2,–9).
“Parabola,” by the way, is not pronounced like “pair of bowlers.” It’s fancier than that, so you have to put the accent on the second “a.”Par. á.bo.la.
—Samantha
Beyond standard and vertex form, there’s something called cartesian form.
This form has the benefit of describing horizontal parabolas (which open left or
right, and are not functions), as well as vertical parabolas (which open up or
down, and are functions).
The cartesian form for vertical parabolas is (x – h)^2 = 4c (y – k)
The cartesian form works because a parabola can be defined geometrically as
a set of points that all have the same distance from the focus (the top dot) as
from the directrix (the dotted line). c is the distance between the vertex (h,k) and
the directrix, and is also the distance between the vertex and the focus.
PERPENDICULAR AND TANGENT LINES
When two lines are perpendicular, they intersect at right angles. You can
immediately tell that two lines are perpendicular if their slopes are opposite
reciprocals of each other. For example, y = – 2x + 6 and are
perpendicular to each other because the slope of the first line is –2 and the slope
of the second is ½.
You will usually see tangent lines associated with circles (or any other conic
section, for that matter, but the SAT’s probably not going to ask about tangents to