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

Apply the properties of operations to generate equivalent expressions.
- 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!
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
- 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!
- 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!
Factor a quadratic expression to reveal the zeros of the function it defines.
- 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!
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
- 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.
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2= q that has the same solutions. Derive the quadratic formula from this form.
- 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!
Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
- 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!
Graph linear and quadratic functions and show intercepts, maxima, and minima.
- 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.

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

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

Note:

Keywords:

Background Tutorials

Apply the properties of operations to generate equivalent expressions.

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Factor a quadratic expression to reveal the zeros of the function it defines.

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2= q that has the same solutions. Derive the quadratic formula from this form.

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Further Exploration

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.