Parabola Vertex Calculator – Find the Vertex

Find the vertex of a quadratic function in standard form:

y = ax² + bx + c

Enter the coefficients a, b, and c, and the calculator determines the vertex coordinates.

What Is the Vertex of a Parabola?

The vertex is the turning point of a parabola.

For a quadratic function:

y = ax² + bx + c

the vertex is:

(h, k)

where:

h = −b / 2a

and:

k = f(h)

How to Use the Calculator

Enter:

• Coefficient a
• Coefficient b
• Constant c

Then click Calculate Vertex.

Example

Consider:

y = x² − 4x + 3

Here:

a = 1
b = −4
c = 3

Calculate x-coordinate:

h = −(−4) / (2 × 1)

h = 2

Then:

k = f(2)

k = 2² − 4(2) + 3

k = −1

So the vertex is:

(2, −1)

Does the Parabola Open Up or Down?

The coefficient a determines the direction.

• If a > 0, the parabola opens upward.
• If a < 0, the parabola opens downward.

Why Find the Vertex?

The vertex can help identify:

• Maximum or minimum values
• Turning points
• Symmetry
• Graph locations
• Important features of quadratic functions

FAQs

Can a equal zero?

No. If a = 0, the equation is linear rather than quadratic.

What does the vertex tell you?

It identifies the parabola’s maximum or minimum point.