Standard form

y = ax² + bx + c

The Vertex form calculator allow you to easily convert a quadratic equation between standard form and vertex form. It is particularly useful for those working with quadratic equations, as it provides a quick and convenient way to switch between the two forms of the equation.

To use the calculator, you just need to enter the values of the coefficients of the equation in the appropriate fields. The calculator will perform the necessary calculations and display the result in the desired form.

The vertex form of an equation is a specific way of writing the equation of a parabola, which is a type of symmetrical, U-shaped curve. In vertex form, the equation of the parabola is written in the form:

y = a(x – h)^{2} + k

where (h, k) is the vertex of the parabola, and a is a coefficient that determines the direction and shape of the parabola.

For example, the equation y = (x + 3)^{2} – 4 describes a parabola with a vertex at (h, k) = (-3, -4). The parabola opens upwards because the coefficient a is positive, and it is stretched vertically because the coefficient a is greater than 1.

The vertex form of an equation is useful because it allows you to easily find the vertex of the parabola, which is a key feature of the curve. You can also use the vertex form of an equation to sketch the shape of the parabola, or to find the roots (or x-intercepts) of the curve.

To convert a quadratic equation from standard form to vertex form, you can follow these steps:

Rewrite the equation in the form y = ax

^{2}+ bx + c, where a, b, and c are the coefficients of the equation.Complete the square.

Simplify the equation by combining like terms on both sides.

Rewrite the equation in the form y = a(x-h)

^{2}+ k, where (h,k) is the vertex of the parabola.