A hovercraft takes off from a platform.
Its height (in meters),
x
xx seconds after takeoff, is modeled by:
h
(
x
)
=
−
3
(
x
−
3
)
2
+
108
h(x)=−3(x−3)
2
+108h, left parenthesis, x, right parenthesis, equals, minus, 3, left parenthesis, x, minus, 3, right parenthesis, squared, plus, 108
What is the height of the hovercraft at the time of takeoff?

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4

answer: do we write it

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for