A vertex form calculator is an online tool designed to make it super easy for you to figure out the vertex form (highest or lowest point) of a quadratic equation, which is essential in graphing and understanding the shape of a parabola curve.
In Mathematics,
“The vertex form is one of the main ways of representing the equation of a parabola, which is a U-shaped curve”.
Before we dive into the Vertex Form Calculator usage, let's quickly understand the concept of a parabola. A parabola is like the shape of a water fountain when it shoots water into the air and then gravity pulls it back down.
It's a curve that describes the concept of a parabola. You can also use a parabola vertex calculator to get this curve for a given second-degree equation.
The formula of vertex form is as follows:
y = a(x - h)² + k
Where,
In this formula,
Let's solve a simple vertex form example step by step:
Vertex Form Equation: y = a(x - h)² + k
Suppose we have the equation: y = 3(x - 2)² + 1
'a' represents the shape of the curve. In this case, it's positive, so the curve opens upward.
'(h, k)' represents the vertex of the parabola. Here, (2, 1) is our vertex. The 'h' value (2) shifts the parabola horizontally, and the 'k' value (1) shifts it vertically. So, our vertex is at (2, 1).
Now, if we want to find 'y' when 'x' is 3, we plug it into the equation:
y = 3(3 - 2)² + 1
First, we calculate inside the brackets:
y = 3(1)² + 1
Then, we square 1:
y = 3(1) + 1
Now, we multiply 3 by 1:
y = 3 + 1
Finally, we add 3 and 1:
y = 4
So, when 'x' is 3, 'y' is 4. This gives us a point on the parabola. You can repeat this process for different 'x' values to plot more points and sketch the parabolic curve. You can also find these values from the vertex calculator.
Using this free online tool vertex form calculator you can easily find the vertex form by entering some inputs such as:
What to do:
What you get:
Here's a list that describes the main differences between vertex form and standard form for quadratic equations:
Vertex Form:
Written as y = a(x - h)² + k.
Standard Form:
Wikihow.com: How to Find the Vertex, Using the Vertex Formula, and Completing the Square
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