Question

Tanya runs a catering business. Based on her records, her weekly profit can be approximated by the function LaTeX: f\left(x\right)=2x^2-44x-150f ( x ) = 2 x 2 − 44 x − 150, where LaTeX: xxis the number of meals she caters. If LaTeX: f(x)f ( x ) is negative, it means that the business has lost money.

How much money did Tanya spend on her catering business?

Answer 1

Answer:She breaks even with the 25th meal when her revenue equals her cost and makes profit with the 26th meal

Explanation:

The function is given as 2x^2 -44x-150 which

is a parabola concave up, whose solutions are 2x^2 -44x-150=0

Then divide through by 2

x^2 -22x - 75 =0

You can use the quadratic formula

-b+square root of b^2 _4ac/2a

Where a =1 b=-22 and c=-75

to find that the solutions of the parabola are

-3 and 25 when you use the quadratic equation

So,if the parabola is negative in the case of -3 .It wouldn't make sense so we only make use of the positive number 25

So, if Tanya caters 25 meals she breaks even, and starting with the 26th meal she will begin to profit.