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BaLLatris [955]
2 years ago
5

Identify the coordinates of the vertex of f(x) = 3x2 + 12x − 8, and identify whether it is an absolute minimum or absolute maxim

um. (2, 28), absolute minimum Correct Answer (−2, −20), absolute minimum Incorrect Response (−2, −20), absolute maximum (2, 28), absolute maximum
Mathematics
1 answer:
DaniilM [7]2 years ago
7 0

The vertex of f(x) = 3x^2 + 12x − 8 is (2,28) absolute minimum

<h3>How to determine the vertex?</h3>

The equation is given as:

f(x) = 3x^2 + 12x − 8

Differentiate the function

f'(x) = 6x + 12

Set to 0

6x + 12 = 0


Divide through by 6

x + 2 = 0

Solve for x

x = -2

Substitute x = -2 in f(x) = 3x^2 + 12x − 8

f(2) = 3 *2^2 + 12 *2 − 8

Evaluate

f(2) = 28

This means that the vertex is (2,28)

A quadratic function is represented as:

f(x) =ax^2 + bx + c

When a is positive, then the vertex of the function is an absolute minimum.

This means that f(x) = 3x^2 + 12x − 8 has an absolute minimum vertex because 3 is positive


Read more about quadratic functions at:

brainly.com/question/18797214

#SPJ1

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<u>Step-by-step explanation:</u>

Cost Function: C(x) = 5.75x + 8,000

              C(10,000) = 5.75(10,000) + 8,000

                                = 57,500     + 8,000

                                = 65,500

Revenue Function: R(x) = 9.50x

                        R(7,850) = 9.50(7,850)

                                       =    74,575

Profit Function: P(x) = R(x) - C(x)

                                 = 74,575 - 65,500

                                 = 9,075

*****************************************************************************

Retail = Unit Cost + Unit Cost × Markup

         =     $375    +         $375 × .75

         =     $375    +           $281.25

         =     $656.25

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$225 but if paid within 10 days there is a 3.5% discount

Discount = $225 - $225 × .035

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               =  $217.13

8 0
3 years ago
Click an item in the list of groups of pictures at the bottom of the problem and, holding the button down, drag it into the corr
tankabanditka [31]

An equation is formed of two equal expressions. The equation of the exponential graph is A=100(0.5)ˣ.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation of an exponential function is given by the formula,

y = A (B)ˣ

Now as per the graph, there are two points (1, 50) and (2, 25).

50 = A (B)¹

50 = AB

A = 50/B

Substitute another point in the equation,.

25 = A (B)²

25 = (50/B) (B)²

25 = 50B

B = 0.5

Substitute the value of B,

A = 50/0.5 = 100

Hence, the equation of the exponential graph is A=100(0.5)ˣ.

Learn more about Equation:

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