Question

While testing a new pesticide, an agricultural scientist uses two functions to predict the yields of two same-sized potato farms that have different soil conditions. The scientist's predicted yield, in tons, of the first farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. His predicted yield, in tons, of the second farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. If the scientist uses the same amount of pesticide on the two farms, select the function that accurately represents the predicted combined yield from both farms.

f(x)= -2.43x^2+10.37x+9 and g(x)= -3.43^2+13x+25


A. h(x)= -5.86x^2 + 23.37x + 34
B. h(x)= -5.86x^2 + 2.63x + 34
C. h(x)= -x^2 + 2.63x + 16
D. h(x)= x^2 + 2.63x - 16

Answer 1

A. h(x)= -5.86x^2 + 23.37x + 34

Explanation:

If the scientist uses the same amount of pesticide on the two farms then the x's of the functions are the same.

Then, the combined yield
`h(x)` of the two farms is just the yield of the first farm plus the yield of the second farm:

`h(x)=f(x)+g(x)`.

Now, since

`f(x)= -2.43x^2+10.37x+9`

and

`g(x)= -3.43x^2+13x+25`,

then

`h(x)= (-2.43x^2+10.37x+9)+(-3.43x^2+13x+25)`

we add the coefficients of the corresponding terms to get:

`h(x)= (-2.43x^2-3.43x^2)+(10.37x+13x)+(9+25)`

`\boxed {h(x)=-5.86 x^2 + 23.37 x + 34.}`

Which is choice A.