How Do You Write a Quadratic Equation in Vertex Form if You Have the Vertex and Another Point?

The word “quadratic” comes from quadratum, which means a square. Hence, we define the quadratic equation as an equation where the variables are of 2nd degree. Therefore, it is also known as the “equation of degree 2”. Quadratic equation is in the form ax2 + bx + c + 0, where x is said to be the unknown variable and a, b, c are the constants and a ≠ 0. In mathematics, it is a problem that deals with a variable, which is multiplied by itself. Sometimes solving the quadratic equations becomes difficult when you don’t know how the numbers work. Simply, use an online vertex form calculator that determines the vertex of the parabola & vertex form of the quadratic equation. 

What is the Quadratic Equation?

The equation is defined as the polynomial equation whose highest degree is two, which is called quadratic equation or quadratics. The equation includes only one unknown variable called “univariate”. The power of the variable “x” is always in a non-negative integer. When you are calculating the quadratic equation in the vertex form, then it might be possible that you go through some calculation issues. You can get rid of these kinds of problems by using the standard to vertex form calculator that instantly shows the vertex & y intercept point along with the graph representation.

Quadratic Equation Formula:

The standard formula for quadratic equations is used to compute the roots of the equations. Since, the degree of the equation is equal to zero; therefore there are two solutions for the equation. Let’s suppose ax2 + bx + c + 0 is the equation, the formula to calculate the roots will be:

x = [-b±√(b2-4ac)]/2

Instead of using this formula to simplify the equation, you can consider the Vertex Form Calculator that helps to find the vertex form, standard form, and characteristic point instantly for the given values.

Quadratic Equation for the vertex form when you have vertex & another point: 

Just like the quadratic equation, the parabola points can help you to write the equation. Parabola has two types of equations, which are standard and vertex. The calculation to write the equation might be complicated. For ease, use an online quadratic vertex calculator that displays the parabola graph with the exact values when the same values are substituted for the vertex equation. For the manual calculations follow the below steps:

  • Recall the vertex form, which is y = a(x – h)2 + k.
  • Now, figure it out what we have been given then, we will be able to know what we still need to find.
  • Plug in the required values in the equation to solve the equation.
  • Use the order of operations to simplify the equation and then solve “a”.
  • After finding all the values for a, h, and k, you can easily write the general equation of parabola by using the vertex form.

The mentioned procedure is time consuming so, you can consider the Vertex Form Calculator to calculate the standard form, characteristic point, and vertex form with the graphical display of points.

Standard Form to vertex Form:

By using the complete square method, you can convert the quadratic equation from the standard form to the vertex.

  • First, you need to write the parabola equation in the standard form.
  • Extract “a” from the first two terms.
  • Now, complete the square for the expression with “x” and simplify the equation.
  • Compress the terms into the shortcut version of multiplication.
  • Remove the brackets of the equation by multiplying the equation with a.
  • Now, compare the outcomes with the vertex form of the equation.
  • As a result of the comparison, we know that how to determine the vertex of a parabola: h = -b/(2a), and k = c – b²/(4a).

 By following this procedure you can easily convert vertex form from the standard form. The second and quicker way of conversion is to use the standard form to vertex form calculator that only requires the values for a, b, and c for the conversion.


In this article, we discussed what a quadratic equation is, its formula, and how to write the equation when a vertex and another point are taken into account. The calculation process is tricky & complicated so, you can use the standard formula for the calculation. In case you are not satisfied with the calculation, then try an online “finding vertex calculator” that can display the vertex and y-intercept point on the graph within a fraction of seconds.

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