Explain the steps necessary to convert a quadratic function in standard form to vertex form

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explain the steps necessary to convert a quadratic function in standard form to vertex form.

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To convert a quadratic function in standard form to vertex form, you can follow the steps below:

Step 1: Write down the quadratic function in standard form. The standard form of a quadratic function is given by the equation: f(x) = ax^2 + bx + c, where a, b, and c are constants.

Step 2: Identify the values of a, b, and c in the quadratic function.

Step 3: Use the formula h = -b/2a to find the x-coordinate of the vertex. The x-coordinate of the vertex is given by h, which represents the value on the x-axis where the vertex is located.

Step 4: Substitute the value of h into the original function to find the corresponding y-coordinate of the vertex. Plug the value of h into the equation f(x).

Step 5: Write down the quadratic function in vertex form. The vertex form of a quadratic function is given by the equation: f(x) = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.

Step 6: Substitute the values of a, h, and k into the vertex form of the quadratic function.

Step 7: Simplify and rewrite the equation in vertex form.

By following these steps, you can successfully convert a quadratic function in standard form to vertex form. This will allow you to easily determine the vertex and other key characteristics of the quadratic function.