Question

f(t)=t^2-6t .. find the domain and sketch the graph.. can somebody explain me how to do this

Answer 1

\[f(t)= t^2-6t\]

Answer 2

When graphing parabolas, it is very useful to put the function into vertex form first then using transformations to determine where the graph is. Do you know about transformations of graphs?

Answer 3

nope

Answer 4

okay that's cool. If you want the simple way just use a graphing calculator.
if not I will try to explain the transformation stuff

Answer 5

i dont have a graphing calculator

Answer 6

or you can find the vertex of the parabola and plot some points and guesstimate the graph

Answer 7

okay I will try to teach you

Answer 8

that is the graph of f(x)=x^2
other quadratic functions or transformations of that graph.
for example, it's moved to the right/left, up/down, stretched...etc.

Answer 9

when you put a quadratic in vertex form you are putting that function in the form
f(x)=(x-h)+k where (h,k) is the vertex

Answer 10

do you know about completing the square to solve quadratics?

Answer 11

can you show me

Answer 12

so completing the square to solve x and doing it to put the function into vertex form is slightly different. More time sake, I will just show putting it into vertex form.
so \[f(x)= t^{2}-6t\]

Answer 13

you want to change this so that you will be able to factor it. To factor it however, you need a constant (the number after -6t) that is (half of 6) squared