How to convert from Vertex to Standard Form?
The Vertex Form of a Parabola isy=a(x-h)²+kwhere (h,k) are the Vertex Coordinates.
The Standard form of a Parabola is
y=ax²+bx+c
Let’s do an easy example first
Let y=2(x-1)²-5we first apply the binomial formula to expand and get
y=2(x²-2x+1)-5
Next, we distribute the 2 to get
y= 2x²-4x+2-5
With 2-5=-3 we finally arrive at the Standard Form:
y=2x²-4x-3
In general, we obtain the Standard Form from the Vertex Form by using these 2 steps:
Given: y=a(x-h)²+k
Step1: (Use Binomial Formula) y=a(x²-2hx+h²)+k
Step2: (Distribute and Combine 2 like terms ah² and k) y=ax²-(2ah)x+(ah²+k)
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: What if the leading coefficient a is negative?

We are given the quadratic equation in vertex format
y=-2(x+3)²-7
First, apply the binomial formula
(x+3)² = x²+6x+9
Thus we have
y= -2(x²+6x+9)-7
Next, distribute the 2 to get
y= -2x²-12x-18-7
Since -18-7=-25 we finally get the standard form
y= -2x²-12x-25
Here, a=-2, b=-12 and c=-25 are the coefficients in the Standard Form
y= ax²+bx+c
Get it now? Try our Vertex to Standard Form Calculator a few more times.