Question

Need the answer asap

The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.
A: 5(x − 7)2 + 13; The minimum cost to produce the product is $13.
B: 5(x − 7)2 + 13; The minimum cost to produce the product is $7.
C: 5(x − 7)2 + 258; The minimum cost to produce the product is $7.
D: 5(x − 7)2 + 258; The minimum cost to produce the product is $258.

Answer 1

f(x)=5x^2-70x+258
Solving by completing square methods gives us:
5x^2-70x=-258
x^2-14x=-51.6
c=(b/2a)^2
c=(-14/2)^2
c=49
x^2-14x+49=-51.6+49
(x-7)(x-7)=-2.6
(x-7)^2=-2.6
multiplying through by 5 you get:
5(x-7)^2+13=0
The answer is:
A] 5(x − 7)2 + 13; The minimum cost to produce the product is $13.