A company's profits can be modeled by a quadratic function. In the past, it broke even (made zero profit) when it fulfilled 240 or 880 orders. If the maximum profit earned was $204,800, complete the function that models the profits of the company, where x is the number of orders fulfilled, and f(x) is the profit earned.

or

Step-by-step explanation:

Let

f(x) ----> the profit earned

x ---> is the number of orders fulfilled

we know that

The equation of a quadratic equation in vertex form is equal to

where

a is the leading coefficient of the quadratic equation

(h,k) is the vertex

Remember that

The x-intercepts or roots are the values of x when the value of the function is equal to zero

In this problem

The x-intercepts are

x=240 and x=880

The x-coordinate of the vertex (h) is the midpoint of the roots

so

The y-coordinate of the vertex (k) is the maximum profit earned

----> is given

so

The vertex is the point (560,204,800)

substitute in the quadratic equation

Find the value of a

we have the ordered pairs (240,0) and (880,0) (the x-intercepts)

take the point (240,0) and substitute the value of x and the value of y in the quadratic equation

solve for a

therefore

The function that models the profits of the company is given by

----> equation in vertex form

Convert to standard form

if this is really you s much. i only have 3 points left and i have 2 questions to ask

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .