Question

Will Give Medal!

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.

5(x − 7)2 + 13; The minimum cost to produce the product is $13.
5(x − 7)2 + 13; The minimum cost to produce the product is $7.
5(x − 7)2 + 258; The minimum cost to produce the product is $7.
5(x − 7)2 + 258; The minimum cost to produce the product is $258.

Answer 1

5x^2-70x+258
5x^2-70x = 5(x^2-14x)
= 5(x^2-14x+49 -49)
= 5( x-7)^2 - 245

5x^2-70x+258 = 5(x-7)^2 -245+258
5(x-7)^2+13

The vertex is (7,13) and the parabola slopes upward because the coefficient of x^2 is positive.
Therefore, (7,13) is a minimum point
5(x − 7)2 + 13; The minimum cost to produce the product is $13.5x^2-70x+258
5x^2-70x = 5(x^2-14x)
= 5(x^2-14x+49 -49)
= 5( x-7)^2 - 245

5x^2-70x+258 = 5(x-7)^2 -245+258
5(x-7)^2+13

The vertex is (7,13) and the parabola slopes upward because the coefficient of x^2 is positive.
Therefore, (7,13) is a minimum point
5(x − 7)2 + 13; The minimum cost to produce the product is $13.

Answer 2

Thank you so much! That really helped! (:

Answer 3

yw