Question

Rewrite the function by completing the square:
f(x)= x^2+x-30
(in fraction form)

Answer 1

To rewrite the function f(x) = x^2 + x - 30 by completing the square, follow these steps: Ensure that the coefficient of the x^2 term is 1. Add the square of half of the coefficient of the x term to both sides of the equation. Factor the perfect square trinomial on the right side of the equation. Write the equation in fraction form, if desired. In this case, the function f(x) = x^2 + x - 30 can be rewritten as f(x) = (x + 0.5)^2 - 30.25 in fraction form.

Step-by-step explanation:

To rewrite the function f(x) = x^2 + x - 30 by completing the square, follow these steps:

1. Ensure that the coefficient of the x^2 term is 1. If it's not, divide the entire equation by the coefficient.
2. Add the square of half of the coefficient of the x term to both sides of the equation.
3. Factor the perfect square trinomial on the right side of the equation.
4. Write the equation in fraction form, if desired.

In this case, the function f(x) = x^2 + x - 30 can be rewritten as f(x) = (x + 0.5)^2 - 30.25 in fraction form.