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.

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nktselepov nktselepov · Answer 1 · 2020-04-11T21:25:52+02:00

The minimum of a quadratic function, with a positive coefficient a, is its vertex.

Let's find the x₀ coordinate.

[tex]f(x) = 5x^2 -70x + 258\\\\x_0=\dfrac{-b}{2a}=\frac{-(-70)}{2*5} =\frac{70}{10} =7[/tex]

Now we need to find y₀ coordinate. That will be the minimum of function.

[tex] y_0=5\times7^2-70\times7+258=13[/tex]

So, the minimum cost to produce the product is $13

Decompose 5x^2 − 70x + 258 into multipliers

[tex]5x^2 - 70x + 258=(5x^2-70x+245)+13=5(x^2-14+49)+13=\\=5(x-7)^2+13[/tex]

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

joshuaclemonsjr joshuaclemonsjr · Answer 2 · 2021-04-29T01:04:48+02:00

Answer:

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

Step-by-step explanation:

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