Convert to Vertex Form Calculator – Convert Quadratic Equations

Convert a quadratic equation from standard form to vertex form. Enter the coefficients a, b, and c from y = ax² + bx + c, and the calculator shows the equivalent vertex-form equation.

What Is Vertex Form?

A quadratic function can be written in vertex form as:

y = a(x − h)² + k

The vertex is:

(h, k)

Vertex form makes the vertex and direction of the parabola easier to identify.

Standard Form vs. Vertex Form

Standard form:

y = ax² + bx + c

Vertex form:

y = a(x − h)² + k

The calculator converts between these forms.

How to Use It

Enter:

• a
• b
• c

Then click Convert to Vertex Form.

Formula

The x-coordinate of the vertex is:

h = −b / 2a

The y-coordinate is:

k = c − b² / 4a

The resulting equation is:

y = a(x − h)² + k

Example

For:

y = x² − 4x + 3

we have:

a = 1
b = −4
c = 3

Therefore:

h = 2

k = −1

The vertex form is:

y = (x − 2)² − 1

Why Use Vertex Form?

Vertex form makes it easier to identify:

• Vertex
• Maximum or minimum
• Axis of symmetry
• Direction of opening
• Graph transformations

FAQs

Is vertex form equivalent to standard form?

Yes. They represent the same quadratic function in different forms.

What is the axis of symmetry?

For vertex form y = a(x − h)² + k, the axis of symmetry is x = h.