The function f(t) = t2 + 4t − 14 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) Part C: Determine the axis of symmetry for f(t). (2 points)

A)  The vertex ( h , k) = ( -2 , -18)

B) The minimum value of the given function = - 18

C) The Axis of the symmetry for f(t) is y -axis

Step-by-step explanation:

A)

Given a parabola   f(t) = t² + 4 t − 14

                               f(t) =  t² + 2(2) t + (2)²-4− 14

                           f(t) = (t +2)² - 18

Let comparing  y = (x +2)² -18

                   (x +2)² = y + 18

                   (x-h))² = 4 a ( y - k))²

The vertex ( h , k) = ( -2 , -18)

B)

  Given a parabola   f(t) = t² + 4 t − 14

  Differentiating with respective to 't'

                                 f¹(t) = 2 t + 4

                                  f¹(t) = 2 t + 4 = 0

now                      

Again Differentiating with respective to 't'

f(x) has a minimum value at t = -2

Given f(t) = t² + 4 t − 14

         f( -2) = 4 + 4(-2) -14 = 4 -8 -14 = -18

The minimum value of the given function = - 18

C)

f(t) = (t +2)² - 18

Let comparing  y = (x +2)² -18

                   (x +2)² = y + 18

                   (x-h))² = 4 a ( y - k))²

The vertex ( h , k) = ( -2 , -18)

The Axis of the symmetry for f(t) is y -axis

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !

, 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