What are the formulas for each of the five key parts of a parabola?

Question

I need to know in about 5 minutes :\

the 5 key parts are the y-intercept, the x-intercepts at most, the axis of symmetry, the vertex, and the point symmetric to the y-intercept. I know how to find all of them except the vertex....somehow im supposed to figure it out by using the axis of symmetry and not the vertex formula. HELP!

Answer 1

Segment of a Parabola


Height: h
Chord length: c
Area: K
Length: s

s = c[1+2(2h/c)2/3-2(2h/c)4/5+...]
s = sqrt[4h2+c2/4]+[c2/(8h)]
ln[(2h+sqrt[4h2+c2/4])/(c/2)]
K = 2ch/3
K = 4T/3, where T is the area of
the triangle formed by the chord
and the point of tangency of a
tangent to the parabola parallel
to the chord



.5 Additional Properties of Parabolas
Let C be the parabola with equation y=4ax, and let F=(a,0) be its focus.


Let P=(x,y) and P'=(x',y') be points on C. The area bounded by the chord PP' and the corresponding arc of the parabola is


It equals four-thirds of the area of the triangle PQP', where Q is the point on C whose tangent is parallel to the chord PP' (formula due to Archimedes).

The length of the arc from (0,0) to the point (x,y) is



The polar equation for C in the usual polar coordinate system is


With respect to a coordinate system with origin at F the equation is



where l=2a is half the latus rectum.

Let P be any point of C. Then the ray PF and the horizontal line through P make the same angle with the tangent to C at P. Thus light rays parallel to the axis and reflected in the parabola converge onto F (principle of the parabolic reflector).

want to try the sites?

Answer 2

I HAVE NO FREAKIN IDEA!!!!