Question

Re write quadratic function into vertex form calcaultor.

Answer 1

To rewrite a quadratic function into vertex form, complete the square and follow the steps: identify the values of a, b, and c, find h and k using the formulas, and substitute the values into the vertex form equation.

Step-by-step explanation:

Quadratic Function in Vertex Form

To rewrite a quadratic function into vertex form, you 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 coordinates of the vertex. Follow these steps:

1. Identify the values of a, b, and c in the standard form equation, y = ax^2 + bx + c.
2. Find the values of h and k using the formulas: h = -b/2a and k = f(h).
3. Substitute the values of h and k into the vertex form equation to obtain the rewritten quadratic function.

For example, let's rewrite the quadratic function f(x) = x^2 - 4x + 3 into vertex form:

1. a = 1, b = -4, c = 3.
2. h = -(-4) / (2 * 1) = 2.
3. k = f(2) = 2^2 - 4(2) + 3 = -1.
4. Vertex form: f(x) = (x - 2)^2 - 1.