The table below contains the values of the function.

Question

The table below contains the values of the function y=f(x).

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

f(x) 0 | 0.5 | 2 | 4.5 | 8 | 12.5 | 18 | 24.5 |

Each function in parts (a)-(c) is a translation (horizontal/vertical/or both) of f(x). In each case the function can be written in the form y=f(x+h)+k, where h and k denote the corresponding horizontal and vertical shifts. For each of the tables below find a possible formula by applying transformations to f(x).

b)

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

g(x) | -1 | 0 | 0.5 | 2 | 4.5 | 8 | 12.5 | 18 |

g(x) =

c)

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

m(x) | 1 | 2 | 2.5 | 4 | 6.5 | 10 | 14.5 | 20 |

m(x) =

Answer 1

a(x-h)^2 +k

f(0)=0 vertex=(h,k)=(0,0) a=1/2

f(x)= .5(x-0)^2 +0

f(x)=.5x^2

g(x)=.5(x-1)^2

shift f(x) right 1, to get g(x)

m(x)=.5(x-1)^2 +2

shift g(x) up 2 to get m(x)