Vertex calculator by calculator-online.net is a tool that helps you to calculate the coordinates of the vertex point for a specific parabola equation in a matter of seconds. If the coefficient x2 is positive then the vertex will be at the bottom of the curve and if it is negative then the vertex will be at the top of the curve.
What is the vertex?
The vertex of a parabola is the point that shows the value of a quadratic curve. The standard form of the parabola is y = ax2 + bx + c and the vertex form is y = a(x – h)2 + k. Quadratic part is vital because the most significant power of the standard parabola is two. You can also say that the vertex is the intersection of the parabola and its symmetry axis.
How to Find Vertex?
We can write the quadratic equation as y = ax2 + bx + c in the standard form but the vertex v of the parabola is v= (-b/2a, -D/4a).
Now here D = b2 – 4ac.
The vertex equation of a parabola y = a(x – h)2 + k and the coordinates are (h, k).
Consider you have a parabola equation y = 2x2 + 5x + 4 for which you have to find the coordinates. Let’s move towards the solution of the equation.
y = 2x2 + 5x + 4
a = 2, b = 5, c = 4
The vertex (h, k) = (-b/2a, -D/4a)
H = -b/2a
H = -5/2(2) = -5/4
For the value of the k we have to find out the value of the d first:
D = b2 – 4ac
D =(5)2 – 4(2)(4)
D = 25 – 32 = -7
Now we will put the value of the D to find out the other coordinate:
K = -D/4a
K = 7/4(2) = 7/8
So the values of the coordinates (h, k) = (-5/4, 7/8).
Instead of going through this lengthy calculation, find the vertex calculator on calculator-online.net and perform unlimited calculations without any hassle.
How to convert Standard form to vertex form?
As we have discussed above the standard form of quadratic equation is m = ax2 + bx + c. Here m and x are variables while a, b, and c are the coefficients. It is easy to perform the calculations on the standard form to get the answer but when you have to create the graph then it is better to use the vertex form. The standard vertex form is Q = m(x – h)2 + k. To help you out below we have listed some steps to convert to vertex form.
Follow these steps:
- Write the standard form: m = ax2 + bx + c.
- Have a common from the first two terms: m = a(x2 + bx/a) + c.
- Now complete the square for expression x. Add and subtract from the equation (b/2a)2 :
- m = a[(x2 + bx/a) + (b/2a)2 – (b/2a)2] + c.
- We can write it as: m = a[(x + (b/2a)2 – (b/2a)2] + c.
- m = a[(x + (b/2a)2 – (b2 /4a)] + c.
Now by comparing it with the vertex form: m = a(x – h)2 + k, the vertex h= -b/2a and k = c-b2 /4a.
Alternatively, get the assistance of an online vertex calculator that lets you perform to and from vertex conversions with a couple of easy steps.
How to Convert vertex form to standard form:
An online vertex formula calculator can easily perform this conversion for you but if you want to do that manually then don’t worry we have listed the steps below:
Lets see the steps:
- Write the vertex form equation: m = a(x – h)2 + k.
- Now expand the square formula: m = a(x2+h2 -2xh) + k.
- Open the brackets: m = ax2+ah2 -2axh + k.
- Compare the quadratics in vertex form: m = ax2 + bx + c.
The vertex of parabola: h = -2ah and k = ah + k.
How to find the vertex with an online Vertex Calculator?
Go through the following simple steps to accurately get the vertex from the free online Vertex form calculator:
Add the values of coefficients a, b, and c in the specified fields.
Choose “use vertex form” if your equation is in vertex form or “convert standard to vertex form” if the equation is in standard form from the drop-down menu.
Press the calculate button and you will see the results on your screen.
Click on the download icon to export the results in PDF format.