Vertex Calculator

Vertex Calculator

Standard Equation y = ax² + bx + c
Enter the Respective Values below

Enter the value of ‘a’

Enter the value of ‘b’

Enter the value of ‘c’

The coordinates of the vertex (h, k)

h =

k =

Vertex Calculator is a free online tool that displays the coordinates of the vertex point for the given parabola equation. BYJU’S online vertex calculator tool makes the calculation faster, and it displays the vertex coordinates in a fraction of seconds.

How to Use the Vertex Calculator?

The procedure to use the vertex calculator is as follows:

Step 1: Enter the values “a”, “b”, “c” in the respective input field

Step 2: Now click the button “Solve” to get the coordinates

Step 3: Finally, the vertex coordinates will be displayed in the output field

What is Meant by Vertex Coordinates?

In conic sections, the parabola vertex is a point where the parabola crosses its axis of symmetry. We know that the standard equation of a parabola is y = ax²+bx+c. If the coefficient of the term x² is positive, the vertex will be in the bottom of the U- shaped curve. If the coefficient of the term x² is negative, the vertex point will be in the top of the U-shaped curve. The standard equation of the parabola in terms of vertex equation is given by:

 y = a(x-h)² + k

Also, read: Conic Sections – Parabola

Example

Question:

Determine the coordinates of the vertex for the given parabola equation: y= 3x²+12x -12

Solution:

Given equation: y= 3x²+12x -12

Here a = 3, b = 12

We know that the formula to find the x- coordinate is given by -b/2a

= -12/2(3)

= -2.

Therefore, x -coordinate is -2

Now, substitute the value of x in the given equation, we get y= -24

Hence, the vertex coordinates (h, k) is (-2, -24)