What you will learn in this mini lessonYou will learn how the 3 different forms of Quadratic Equations and their uses. Our Step by Step Calculators allow you to convert your quadratic equation from one form to another.
Quick Example: Convert from Standard to Factored Form
2x2 -12x+16 Factor out 2:
= 2(x2 -6x+8)
= 2(x-4)*(x-2) since (-4) + (-2) = -6 and (-4)*(-2)=8
That’s all 😉
What are the 3 different Forms of Quadratic Equations?There are 3 different forms of Quadratic Equations:
y = ax²+bx+cVertex Form:
y = a(x-h)²+k(h,k) = Vertex Coordinates.
y = a(x-r)(x-s)r and s = Zeros of the Parabola.
Example of the 3 different forms?
y = x²+6x+8can be rewritten in Vertex Form:
y = (x+3)²-1It tells us that above Parabola has Vertex Coordinates = (3,-1).
The process to convert from Standard Form to Vertex Form is called “Completing the Square”. You can Complete the Square for your quadratic equation here: You can read the details and examples on how to convert here:
y = (x+4)(x+2)It tells us that above Parabola has Zeros -4 and -2 .
The process to convert from Standard Form to Factored Form can be done here: You can read the details and examples on how to convert here.
Or simply use the head menu when converting between the different Parabola Forms.
How do I convert from Vertex Form to Standard Form?The Vertex Form of a Parabola is
y=a(x-h)²+kwhere (h,k) are the Vertex Coordinates.
The Standard form of a Parabola is
Let’s do an easy example firstLet y=2(x-1)²-5
we first apply the binomial formula to expand and get
Next, we distribute the 2 to get
With 2-5=-3 we finally arrive at the Standard Form:
In general, we obtain the Standard Form from the Vertex Form by using these 2 steps:
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)
We created a separate page for you that teaches the Vertex to Standard Form Conversion. It also has a Solver that allows you convert you Vertex Form Equation into Standard Form. Visit our page here.