The vertex form of an equation is another method to find out the equation of a parabola. Typically, you will notice a standard quadratic equation is written as ax^2+bx+c when the graph will become in the form of a parabola. With the help of this graph, it’s easy sufficiently to calculate the roots of the equation (when the parabola strikes the x-axis) by specifying the equation equal to zero (or using the quadratic formula). An online vertex form calculator allows you to discover the vertex of a parabola as well as the vertex form of a quadratic equation.
Standard Form and Vertex Form of a Parabola:
The equation of a parabola can be expressed in considerable ways such as standard form, vertex form, and intercept form. One of these forms can always be converted into one another two forms that primarily depend on the need. In this article, you will learn about the procedure of how to convert standard form equations to vertex form by using the convert to vertex form calculator.
It’s important first to explore what each of these forms represents. Let’s find:
The standard form of a parabola is:
y = ax^2 + bx + c
Where, a, b, and c are whole numbers (constants) where a ≠ 0. x and y are variables where (x, y) expresses a point on the parabola graph.
Likewise, the vertex form of a parabola is:
y = a (x – h)^2 + k
Where, a, h, and k are real numbers, where a ≠ 0. x, and y are variables where (x, y) represents a point on the parabola.
However, an online standard to vertex form calculator supports both the formulas of standard form and vertex form.
In both forms, y represents the y-coordinate, x represents the x-coordinate, and a is the constant that tells you whether the parabola is encountering up (+a) or down (−a). (I assume about it as if the parabola was a bowl of applesauce; if there’s a +a, I can add applesauce to the bowl; if there’s a −a, I can bounce the applesauce out of the bowl.)
The primary difference between a parabola’s standard form and vertex form is that the vertex form of the equation also shows you the parabola’s vertex: (h,k). Also, you can find the difference with the assistance of an online vertex to standard form calculator.
How to Convert Standard Form to Vertex Form?
In the vertex form, y = a (x – h)^2 + k, there is a “whole square”. Therefore to convert the standard form to vertex form, you need to complete the square of the given equation. Besides that, you have also a formula method for accomplishing this. A free standard form to vertex form calculator is the best source to change standard form into vertex form. Let’s look into both processes.
By Completing the Square:
Let’s assume an example of a parabola in standard form: y = -3×2 – 6x – 9 and convert it into the vertex form by completing the square.
First, you should ensure that the coefficient of x^2 is 1. In case the coefficient of x^2 is NOT 1, then you will recognize the number further as a common factor. You will get:
y = −3×2 − 6x − 9 = −3 (x2 + 2x + 3)
Now, the coefficient of x^2 is 1. Here are several steps to convert the above term into the vertex form.
Step 1: First, determine the coefficient of x.
Step 2: Assemble it in half and square the consequent number.
Step 3: Then, add and subtract the above digit once the x term is in the expression.
Step 4: After that, factorize the perfect square trinomial assembled by the first 3 terms utilizing the appropriate identity.
Here, you could use x^2 + 2xy + y^2 = (x + y)^2.
In this case, x^2 + 2x + 1= (x + 1)^2
The above equation from Step 3 evolves:
Step 5: Now simplify the last two numbers and divided the outside number.
Here, -1 + 3 = 2. Therefore, the given expression becomes:
This is of the form y = a (x – h)2 + k, which is in the vertex form. And, the vertex is, (h, k)=(-1,-6).
However, an online vertex form calculator provides a simple and more convenient way to perform the calculations.