Complete the square to rewrite the function f(x)=2x2+20x+54 in the form f(x)=a(x–h)2+k.f(x)=Complete the sentence below.The function f(x) has a minimum value of , which occurs when x=.SubmitQuestions

To rewrite the function f(x)=2x^2+20x+54 in the form f(x)=a(x–h)^2+k, we first need to complete the square. Here are the steps:

1. Divide all terms by the coefficient of x^2, which is 2. This gives us f(x) = x^2 + 10x + 27.

2. Rearrange the equation to group the x terms together: f(x) = x^2 + 10x + 27.

3. To complete the square, we need to add and subtract (b/2)^2 inside the parenthesis, where b is the coefficient of x. In this case, b is 10, so (b/2)^2 = (10/2)^2 = 25.

4. Add and subtract 25 inside the parenthesis: f(x) = (x^2 + 10x + 25) - 25 + 27.

5. Simplify the equation to get it in the form f(x)=a(x–h)^2+k: f(x) = (x + 5)^2 + 2.

So, the function f(x)=2x^2+20x+54 can be rewritten as f(x) = 2(x + 5)^2 + 2.

The function f(x) has a minimum value of 2, which occurs when x = -5.