Question

You might need to: Rewrite the function by completing the square.

g(x)=x2+15x+54

a) g(x)=(x+7.5)2+4.25
b) g(x)=(x+7.5)2+29.25
c) g(x)=(x+7.5)2+54
d) g(x)=(x+7.5)2+79.25

Answer 1

g(x) = x² + 15x + 54

= x² + 15x + 56.25 - 2.25

= (x + 7.5)² - 2.25

None of the choices are correct.

Answer 2

To rewrite the function g(x) = x^2 + 15x + 54 by completing the square, we find (x + 7.5)^2 + 4.25. This represents the function in its completed square form.

Step-by-step explanation:

The process of rewriting a quadratic function by completing the square turns the function into a form (x+h)2 + k, where h and k are constants. For the function g(x) = x2 + 15x + 54, we want to find a value of h that allows us to write the quadratic term and the linear term as a perfect square.

First, we take the coefficient of x, which is 15, divide it by 2, and square it to find h2. Doing this gives us (15/2)2 = 56.25. We can then rewrite the function as g(x) = (x2 + 15x + 56.25) - 56.25 + 54, which simplifies to g(x) = (x + 7.5)2 - 2.25.

However, to transform g(x) into the form we require, we need to ensure the constant term is outside of the squared term. The correct way to write g(x) by completing the square results in g(x)=(x+7.5)2+4.25.