得新的二次函數為_________。

Question

1.二次函數y=-2x ²:

(1)向右平移3單位，得新的二次函數為______。

(2)承(1)，再向下平移4單位，得新的二次函數為_________。

Answer 1

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交大游凱復的心得整理:Operations on polyhedra

Elements are given from the seed (v,e,f) to the new forms, assuming seed is a convex polyhedron: (a topological sphere, Euler characteristic = 2)

Operator Name Alternate

construction vertices edges faces Description

Seed v e f Seed form

r Reflect

(Hart) v e f Mirror image for chiral forms

d dual f e v dual of the seed polyhedron - each vertex creates a new face

a ambo e 2e 2 + e The edges are new vertices, while old vertices disappear. (rectify)

j join da e + 2 2e e The seed is augmented with pyramids at a height high enough so that 2 coplanar triangles from 2 different pyramids share an edge.

t truncate dkd 2e 3e e + 2 truncate all vertices.

-- -- dk 2e 3e e + 2 Dual of kis, (bitruncation)

-- -- kd e + 2 3e 2e Kis of dual

k kis dtd e + 2 3e 2e raises a pyramid on each face.

c chamfer e + v 4e 2e + f New hexagonal faces are added in place of edges.

- - dc 2e + f 4e e + v

e expand aa 2e 4e 2e + 2 Each vertex creates a new face and each edge creates a new quadrilateral. (cantellate)

o ortho de 2e + 2 4e 2e Each n-gon faces are divided into n quadrilaterals.

p propellor

(Hart) v + 2e 4e e + f A face rotation that creates quadrilaterals at vertices (self-dual)

- - dp e + f 4e v + 2e

s snub dg 2e 5e 3e + 2 "expand and twist" – each vertex creates a new face and each edge creates two new triangles

g gyro ds 3e + 2 5e 2e Each n-gon face is divided into n pentagons.

b bevel ta 4e 6e 2e + 2 New faces are added in place of edges and vertices, Omnitruncation (Known as cantitruncation in higher polytopes).

m meta db & kj 2e + 2 6e 4e n-gon faces are divided into 2n triangles

Special forms

The kis operator has a variation, kn, which only adds pyramids to n-sided faces.

The truncate operator has a variation, tn, which only truncates order-n vertices.

The operators are applied like functions from right to left. For

Answer 2

1.二次函數y=-2x ²:

(1)向右平移3單位，得新的二次函數為

y =-2(x-3)^2

(2)承(1)，再向下平移4單位，得新的二次函數為

y =-2(x-3)^2 - 4