Completing the Square in a Quadratic Expression Worksheets
Quadratic equations are polynomials of the second degree. Because of this, they are often a bit more complicated to solve. On top of that, they have two solutions which can be visualized on a graph of them because their graphs form a parabola. There are four widely accepted methods for solving them and all of these methods set the equation equal to zero. We usually start off solving them by simply factoring. We then learn how to use the quadratic formula to put these things to rest. You can also graph them and see where their intercepts lie. For quadratic equations that have a lead coefficient of one we can use this method called completing the square that rearranges the equation, so the lead side becomes a perfect square trinomial. These worksheets and lessons have students add a term to convert a quadratic expression into a square of a binomial.
Aligned Standard: HSA-SSE.B.3b
- Missing Parts Step-by-step Lesson- You need to create a square quadratic by adding terms that are currently blank.
- Guided Lesson - Once again, solve each problem by supplying the lost term.
- Guided Lesson Explanation - Everything on here will give you any idea of the level of patience that you will need to complete these regularly.
- Practice Worksheet - A let drill and kill always helps us get better.
- Matching Worksheet - Match the partial quadratics to their missing pieces.
- Completing the Square Five Worksheet Pack - A very large practice pack for you to work away at.
- Answer Keys - These are for all the unlocked materials above.
It is definitely best to start off slow with this one.
- Homework 1 - Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
- Homework 2 - We are missing the whole number portion of the quadratic.
- Homework 3 - Find the missing value to create a perfect-square.
I provided a lot of space for students to put their work on these.
- Practice 1 - What is missing?
- Practice 2 - Lots of new variables for you to play with.
- Practice 3 - What whole number is missing from each expression?
Math Skill Quizzes
After the first quiz, they should have this skill down pat.
- Quiz 1 - Lots of holes in here, like Swiss cheese.
- Quiz 2 - You will need to find variables too.
- Quiz 3 - That y variable is a mess.
How to Complete the Square in a Quadratic Equation
Quadratic equations are second degree equations that follows the general backbone of: ax2 + bx + c = 0 into something like this: a(x + d)2 + e = 0. For those who don't know, D = b/2a and e = c - (b2/4a)
There are a number of different ways to process these equations and determine their overall value. We have previously explored the use of the quadratic formula. On this topic page we have chose to explore another method called Completing the Square. This is where reshape the equation so that the left side of it forms a perfect square trinomial. It should be noted that this method only works for equations where the lead coefficient is 1. I do see many people attempt to work this through on equations that do not follow this form and it is a bit of a monster.
There are several steps that we would take to solve using this method. If we were solving the quadratic: ax2 + bx + c = 0 we would follow these steps:
1. Get the variable (c) by itself. In this, case simply subtract.
2. Divide both sides by the leading coefficient (a).
3. Add the square of the half the coefficient of the x term to both sides.
4. Factor, if possible.
5. Take the square root of both sides to remove the exponent.
6. Get x by itself.
Suppose that you have an equation like this x2 + bx if you have X twice in the equation that can make solving the equation a bit tricky. So, what can be done? Taking some inspirations from the rules of geometry, we can convert it like this: x2 + bx can be converted to nearly a square. In algebraic form it will look something like this: x2 + bx + (b/2)2 = (x+b/2)2
Hence, completing the square. So, when you add (b/2)2 , the square can be completed and (x + b/2)2 has x only once which is far easier to use.