Determine the quadratic function whose graph is given.

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The vertex is (1,2)

The y-intercept is (0,-9)

F(x)= ?

Oct 12th, 2015

Thank you for the opportunity to help you with your question!

The equation of a vertex has the form:

F(x)=a(x-h)^2 + k, where (h,k) is the vertex of the parabola

The Vertex is (1,2)

F(x)=a(x-1)^2 + 2 = a(x^2-2x +1) +2

                               =ax^2 -2ax +a + 2

                               =ax^2 - 2ax +(a+2)

                               Given a quadratic of the from ax^2 + bx +c

                              see that

                              b = -2a

                              c=(a+2)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 12th, 2015

I am confused as to what the answer is?

Oct 12th, 2015

I'm very happy to clarify


Oct 12th, 2015

what does f(x)=?

Oct 12th, 2015

I can simplify further as follows

y intercept is always of the form (0, c) meaning (0,-9) means c=-9

From above

c=a+2

-9 = a+2

a=-9-2=-11

Then

b=-2a=-2*-11=22

Therefore

Oct 12th, 2015

f(x) =ax^2 - 2ax +(a+2)

f(x)=-11x^2 +22x-9

Oct 12th, 2015

The monthly revenue R achieved by selling x wristwatches is figured to be R(x)=85x-0.2x^2. The monthly cost C of selling x wristwatches is C(x)=32x+1850. 

A. How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue?

B. Profit is given as P(x)=R(x)-C(x). What is the profit function? 

C. How many wristwatches must the firm sell to maximize profit? What is the maximum profit?


Oct 12th, 2015

A: Find the slope of R(x) and set it equal to zero

    d/dx(85x-0.2x^2)=0

           85-0.4x=0

           -0.4 x = -85

              x=212.5

    The maximum revenue is

Oct 12th, 2015

R(x)=85x-0.2x^2

R(212.5) = 85 * 212.5 -0.2 * 212.5*212.5

               =18062.5-9031.25

               =9031.25

B.

Oct 12th, 2015

B. P(x)=R(x)-C(x) =85x-0.2x^2-32x-1850

    P(x) = 85x-32x-0.2x^2-1850

            =53x-0.2x^2-1850  This is the profit function


C.


 


Oct 12th, 2015

C. Find the slope of the profit function:

    d/dx(53x-0.2x^2-1850)=0

          53-0.4x=0

            -0.4x=-53

              x=-53/-0.4

               x=132.5


Oct 12th, 2015

The maximum profit is:

P(132.5)=53*132.5 -0.2*132.5*132.5-1850

              =7022.5-3511.5-1850

              =1661.25

Oct 12th, 2015

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