The cost to produce a product is modeled by the function f(x) = 5x^2 − 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.

i thiink its b

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

f(x) = 5x^2 − 70x + 258

= 5(x^2 - 14x + 49-49) + 258
= 5(x-7)^2 - 245 + 258
= 5(x-7)^2 + 13
my choice is a)

The minimum cost is 13, obtained when x = 7

You are correct! The correct answer is:

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

Yes, you are correct. The minimum cost to produce the product is $7 based on the given function f(x) = 5x^2 − 70x + 258.

To find the minimum cost, we need to complete the square. Here's how:

Step 1: Take the coefficient of x^2, which is 5, and factor it out: f(x) = 5(x^2 − 14x) + 258.
Step 2: Take half of the coefficient of x, which is -14, square it, and add it inside the parentheses: f(x) = 5(x^2 − 14x + (-14/2)^2) + 258.
= 5(x^2 − 14x + 49) + 258.
Step 3: Simplify the expression inside the parentheses by factoring it as a perfect square: f(x) = 5(x − 7)^2 + 258.

Now we can see that the minimum cost occurs when (x − 7) equals 0, as a perfect square is always positive or zero. So the minimum cost is 5(0)^2 + 258 = 258.

Therefore, option b: 5(x − 7)^2 + 13; The minimum cost to produce the product is $7 is incorrect. The correct answer is option c: 5(x − 7)^2 + 258; The minimum cost to produce the product is $258.