Quadratic Vertex Form Converter

How to calculate the Vertex Form?

The vertex form of a quadratic function is obtained by completing the square on the standard form equation ax² + bx + c. This mathematical process rearranges the equation into the form a(x - h)² + k, which reveals the vertex (h, k) of the parabola directly.

Alternatively, you can solve for the coordinates of the vertex using these formulas:

h = -b / (2a)

k = c - (b² / 4a)

Using the converter: an example

Consider a quadratic equation where a = 1, b = -4, and c = 3 (Standard Form: y = x² - 4x + 3).

Step-by-step calculation:

1. Find h: Calculate h = -(-4) / (2 * 1) = 2.
2. Find k: Plug h into the original equation: k = (2)² - 4(2) + 3 = -1.
3. Write the Final Form: The vertex form is y = 1(x - 2)² - 1.

Frequently Asked Questions

What is the vertex form?

It is a way of writing quadratic functions that highlights the vertex coordinates. This is useful for identifying the maximum or minimum value of the function instantly.

What does 'a' represent?

The 'a' coefficient is the same in both standard and vertex forms. It tells you if the parabola opens up (positive) or down (negative) and how steep the curve is.

How do I find intercepts from vertex form?

To find the y-intercept, evaluate the function at x = 0. To find the x-intercepts, set y = 0 and solve for x using square roots or the quadratic formula.