Two quadratic functions are shown.

function 1:

f(x) = 4x2 + 8x + 1

function 2:
x g(x)
−2 2
−1 0
0 2
1 8

which function has the least minimum value and what are its coordinates

The least minimum value is attained by:

First function---- f(x)

Coordinate of the point: (-1,-3)

Step-by-step explanation:

We are given a equation of first function as:

The graph of this function is a parabola which is open upward and the vertex of the parabola is at (-1,-3)

Since, the parabola is open upward hence the vertex of the parabola is the point of minima of the parabola.

                 The minimum value of the function f(x) is:

                                   -3

Now we are given a table of values of the second  function i.e. g(x) as:

                          x    g(x)

                        −2     2

                        −1     0

                         0     2

                         1      8

Clearly by looking at the values we see that:

      The minimum value attained by the function g(x) is:

                                         0

The least minimum value is attained by:

First function--- f(x)

The coordinates of the minimum point are:  (-1,-3)

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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