vertex form of a quadratic function
The vertex form of a quadratic function is a way to express a quadratic function (a function of the form f(x) = ax^2 + bx + c) in a simplified and more convenient form
The vertex form of a quadratic function is a way to express a quadratic function (a function of the form f(x) = ax^2 + bx + c) in a simplified and more convenient form. It is represented as f(x) = a(x – h)^2 + k, where (h, k) represents the coordinates of the vertex of the parabola.
In this form, ‘a’ is the coefficient that determines whether the parabola opens upwards (if ‘a’ is positive) or downwards (if ‘a’ is negative). The values of ‘h’ and ‘k’ represent the x-coordinate and y-coordinate of the vertex, respectively.
The vertex form is advantageous because it provides clear information about the vertex of the parabola without having to graph it. Additionally, it allows for easy identification of the axis of symmetry, which is the vertical line passing through the vertex.
To convert a quadratic function from standard form to vertex form, you can use the process of completing the square. Here’s how:
1. Start with a quadratic function in standard form, f(x) = ax^2 + bx + c.
2. Identify the values of ‘a’, ‘b’, and ‘c’.
3. Find the value of ‘h’ by using the formula h = -b/2a. This gives you the x-coordinate of the vertex.
4. Substitute the value of ‘h’ into the equation to find the value of ‘k’. Plug in the value of ‘h’ into f(x) to get f(h).
5. Write the function in vertex form as f(x) = a(x – h)^2 + k, using the values of ‘a’, ‘h’, and ‘k’ that you calculated.
By expressing the quadratic function in vertex form, it becomes easier to understand and work with various properties of the parabola, such as its vertex, axis of symmetry, and direction of opening.
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