Solution with StepsEnter Leading Coefficient a and the Vertex (h,k) in the above 3 boxes.
Next, press the button to convert the Vertex to Standard Form of a Parabola with Steps.
How do you convert from Vertex to Standard Form?The Vertex Form of a Parabola is
where (h,k) are the Vertex Coordinates.
The Standard form of a Parabola is
To obtain the Standard Form from the Vertex Form we use these steps:
Example: To convert
we first apply the binomial formula to get
Next, we distribute the 2 to get
With 2-5=-3 we finally arrive at the Standard Form:
How do you find the Vertex of a Quadratic Equation?Every Parabola has either a..
..Minimum (when opened to the top due to leading coefficient a>0) or
..Maximum (when opened to the bottom due to leading coefficient a<0).
The Vertex is just that particular point on the Graph of a Parabola.
See the illustration of the two possible vertex locations below:
Example: Convert the Vertex Form into the Standard Form?
We are given the quadratic equation in vertex format
First, apply the binomial formula
(x+3)^2 = x^2+6x+9
Thus we have
Next, distribute the 2 to get
Since 18-7=11 we finally get the standard form
Here, a=2, b=12 and c=11 are the coefficients in the Standard Form
Get it now? Try the above Vertex to Standard Form Calculator a few more times.