How Do You Convert a Quadratic from Standard Form to Vertex Form by Completing the Square if a≠1?

Note:

You can change a quadratic equation from standard form to vertex form by completing the square! This tutorial takes you through the process step-by-step.

Keywords:

problem
vertex form
completing the square
quadratic equation
a

Background Tutorials

Polynomial Definitions
- What is a Polynomial?
  
  If you learn about algebra, then you'll see polynomials everywhere! In this tutorial, you'll learn the definition of a polynomial and see some of the common names for certain polynomials.
Quadratic Functions
- What is the Vertex of a Quadratic Function?
  
  Each quadratic equation has either a maximum or minimum, but did you that this point has a special name? In a quadratic equation, this point is called the vertex! Take a look at the vertex of a quadratic equation by watching this tutorial.
Using the Distributive Property
- What is the Distributive Property?
  
  The distributive property is a very deep math principle that helps make math work. It's the rule that lets you expand parentheses, and so it's really critical to understand if you want to get good at simplifying expressions. So check out the tutorial and let us know what you think!
Graphs of Quadratic Functions
- How Do You Find the a, b, and c Values of a Quadratic Function?
  
  When you're dealing with quadratic equations, it can be really helpful to identify a, b, and c. These values are used to find the axis of symmetry, the discriminant, and even the roots using the quadratic formula. It's no question that it's important to know how to identify these values in a quadratic equation. This tutorial shows you how!
Solving Equations by Adding
- What's the Addition Property of Equality?
  
  Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the addition property of equality, and it lets you add the same number to both sides of an equation. Watch the video to see it in action!
Solving Equations by Subtracting
- What's the Subtraction Property of Equality?
  
  Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the subtraction property of equality, and it lets you subtract the same number from both sides of an equation. Watch the video to see it in action!
Definitions for Quadratic Functions
- What is the Standard Form of a Quadratic?
  
  Got a quadratic polynomial? Want to put it in standard form? Watch this tutorial to learn the steps it takes to make sure a quadratic polynomial is in standard form!
Defining Quadratic Equations
- What is a Quadratic Equation?
  
  You can't go through algebra without seeing quadratic equations. The graphs of quadratic equations are parabolas; they tend to look like a smile or a frown. There's also a bunch of ways to solve these equations! Watch this tutorial and get introduced to quadratic equations!
Factoring Strategies
- How Do You Use a Shortcut to Factor a Perfect Square Trinomial?
  
  Factoring a perfect square trinomial? Did you know there's a shortcut to factoring this special kind of trinomial? Check it out! It's pretty cool, and it may make this process a little faster!
- How Do You Factor the Greatest Common Factor out of a Polynomial?
  
  Factoring out the greatest common factor of a polynomial can be an important part of simplifying an expression. In this tutorial, you get step-by-step instructions on how to identify and factor out the greatest common factor.