Question

Write the function in vertex form means complete the square

Answer 1

To write the function in vertex form, we need to complete the square and follow a series of steps. This will help us accurately express the quadratic function in the form f(x) = a(x-h)^2 + k.

Step-by-step explanation:

To write the function in vertex form, we need to complete the square. The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola. To complete the square, we can follow these steps:

1. Make sure the coefficient of the quadratic term is 1. In this case, we have x^2 as the quadratic term, so no adjustment is needed.
2. Group the linear terms together and leave some space after the quadratic term.
3. Take half of the coefficient of the linear term and square it. This will be the value we add and subtract inside the parentheses.
4. Write the quadratic term, followed by the adjusted linear terms inside the parentheses, and then add or subtract the calculated value from step 3.
5. Simplify the expression inside the parentheses, and factor out any common factors.

By following these steps, we can complete the square and write the function in vertex form.