How Do You Write a Quadratic Equation in Vertex Form (Simple Steps):
We can write the quadratic equation ax2+bx+c=ythe vertex form of the quadratic equation can be written as y=a(x-h)2+k, In both the equation we know that “y” is the y-coordinate or y-intercept of the graph, “x” is the x-coordinate or x-intercept of the graph, “a” is a constant value, which is used to determine the parabola is facing up or facing down. We can use a vertex calculator, to find the vertex form from the quadratic form of the parabola.
If we need to convert the vertex form to standard form, a vertex form to standard form calculator would be a good option. The vertex form is a great tool to know the nature of the parabola, we are dealing with, what kind of shape it has, we can determine this only by seeing the vertex form equation. All this information we can collect by converting the equation from the quadratic form to the vertex form.
The upside and downside Parabola:
We know if the value of a is “+a” the parabola would be facing up, if the sign is “-a” the parabola is facing down. If you haven’t been able to understand, What is parabola facing up or facing down, we can understand the concept, if we can app water in the parabola, then it is facing up, it can’t add water into it, then we can say it is facing down. This is great to get information about the parabola, so it is critical to convert the standard form equation to vertex form. We can use the vertex form calculator to find the vertex form of the quadratic equation.
Why we need to find the vertex form of the quadratic equation:
There is a big question here, why do we need to convert the standard form of the parabola ax2+bx+c=y into vertex form, in the vertex form we can also able to find the vertices of the parabola y=a(x-h)2+k, you can see two more variables (h,k) in the vertex form equation, these variables are vertex(h,k) of the parabola. We can convert the standard form to vertex form by a standard form to vertex form calculator, this is necessary to find the vertex of the parabola, as we can’t perfectly draw a parabola on the graph without vertex. It makes our calculations and helps us to understand the equation more easily.
Method of finding the vertex form:
For students it is critical to know the method of converting the standard form to the vertex form manually, we are presenting the step by step calculation of the procedure:
- Now consider a standard form quadratic equation y=7×2+42x+6We want to convert this equation to the vertex form.
- In the first step, we take the value of the constant “c” towards the other side of the equation y=ax2+bx+c, then the equation would become
y-6= 7×2+42x
- Then we take the common at the next step, we get the equation:
y-6= 7(x2+6x)
- Now we need to complete the square inside the small brackets,
y-6= 7(x2+6x+ )
- We can complete the square by adding +9, then the equation would become:
y-6= 7(x2+6x+9 )
- We need to add the same amount on the other side of the equation we get:
y-6+7(9)= 7(x2+6x+9 )
y-6+63= 7(x2+6x+9 )
Now by completing the square we get:
y-57= 7(x+3 )2
y= 7(x+3 )2+57
Method of finding the vertex of a Parabola:
Now we can find the values of vertex(h,k), according to the Vertex form equation
y=a(x-h)2+k
Now the vertex of the parabola is (h,k), (-3,57), we can use these vertices to draw the parabola, we can use the vertex calculator to find the vertex of the parabola even if it is in the standard form.
Diclaimer: This is a guest blog, as we occasionally accept articles/blogs/news from reputable guest authors. The views, opinions, and all other content mentioned in the section are of the guest author and they do not represent the views of Ghani Associate in any way.
