quadric functions and parobolas

Question

the profit (p) in dollars, for a company modeled by the function p(x) = -750x^2 +15,000x, where x is the number of items produced. For which value of x will the company lose money.

 

a. x<2

b. x>20

c. 2<x< 10

d. 10< x <20 

Answer 1

Hey Christine -- the "break-even" point is when p(x) =0 ... Set 750x^2 = (15k)x ...

 

Xbreak-even is 15k over 750 or 20 units. Test p(21) ... p(21) is negative, money-losing ...

 

x> 20 ans. "b" ... Best wishes ma'am :)

Answer 2

Hi Christine;

This is a parabola which opens downs.  It is negative.

The vertex is the highest point.

The range from y=0 to y of the vertex is the profit range---the positive range of the y-axis.

Let's establish the vertex...

x=-b/2a

x=-15,000/2(-750)

The negatives cancel...

x=15,000/1,500

x=10

 

0=-750x²+15,000x

0=-750x(x-20)

If...

0=-750x

Then...

x=0

If...

0=x-20

Then...

x=20

 

The range of profitability is from x>0 and x<20, which includes the vertex of x=10.

 

Therefore, the answer is b. x>20, because this begins the range below the y-axis, the range of loss.

 

a. x<2
b. x>20-------answer
c. 2<x< 10
d. 10< x <20