Exploring the Parabola
Author: Steve Arnold
Date: 18/06/06

What properties of the parabola can you deduce from this worksheet? What is the importance of the points A, B, C and D?

What happens if C does NOT lie at the midpoint of AB?

Move the point B to trace the locus of the parabola which has A as its focus and the x-axis as directrix.
Now use the three sliders to try and match the function to the curve.

Exploring the Parabola

1. Drag the point B to trace out the parabola.

3. Move the point C: what do you notice when
it no longer lies at the centre of AB?

2. Use sliders a, b and c to move the red curve, f1(x),
 to match our parabola.

Drag Me!

A = Point(yAxis)
B = Point(xAxis)
m = Segment(A, B)
C = Point(m)
n = OrthogonalLine(C, m)
o = OrthogonalLine(B, xAxis)
D = Intersect(n, o)
loc1 = Locus(D, B)
d = OrthogonalLine(D, n)
E = Point(o)
e = Ray(D, E)
D' = Mirror(D, d)
E' = Mirror(E, d)
f = Ray(D', E')
a = 1 (slider from -5 to 5, step 0.01)
b = 0 (slider from -5 to 5, step 0.1)
c = 0 (slider from -5 to 5, step 0.1)
f_1(x) = a (x - b)² + c
F = (8, 7)
G = (12, 7)
H = (12, 4)
I = (8, 4)
J = (6, 4)
K = (20, 4)
L = (20, 0)
M = Point(xAxis)
Q, j, k, l, m_1 = Polygon(J, K, L, M)
N = (5, 16)
O = (19, 16)
P = (19, 3)
R = (5, 3)
S, n_1, o_1, p, r = Polygon(N, O, P, R)
T = (-5.033333333333333, -0.8066666666666663)
u = Vector(T, B)