Question

Functions f(x) and g(x) are shown below:

f(x) = x2
g(x) = x2 + 20x + 100

In which direction and by how many units should f(x) be shifted to obtain g(x)?

Answer 1

@abb0t Help please?

Answer 2

@ankit042 Helo please?

Answer 3

do you know what "perfect square trinomial is?

Answer 4

\(\bf f(x) = x^2\qquad \qquad g(x) = x^2 + 20x + 100\)

notice g(x) closely

Answer 5

Yes, f(x) is part of g(x) @jdoe0001

Answer 6

right... do you know what "perfect square trinomial is?

Answer 7

I do it has three parts, one sqared, one x and a regular number
@jdoe0001

Answer 8

well... yes... well, g(x) is a "perfect square trinomial"

so you should be able to make it into a squared binomial like \(\bf (a + b)^2\)

Answer 9

if you were to do so, what would g(x) look like?

Answer 10

Oh so I just factor?
@jdoe0001

Answer 11

yes, just factor it, once you factor, you'll notice the "shifts"

Answer 12

Oh wow okay! Could you help me with another one? @jdoe0001

Answer 13

ok

Answer 14

Water coming out from a fountain is modeled by the function f(x) = -x2 + 6x + 6 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 2 to x = 5 represent?
@jdoe0001

Answer 15

dx/dt represents the speed in this case

Answer 16

... right

Answer 17

I dont understand what im supposed to do @jdoe0001 @ankit042

Answer 18

the average "rate of change" will involve the derivative
which is what ankit042 said, the dx/dt

Answer 19

find f(2) and f(5)
now rate of change = (f(5)-f(2))/(5-2)