Quadratic Equation Worksheets
What are Quadratic Equations? Students have to deal with a lot of different types of equations. The most basic form of an equation is linear where the highest power of the variable is 1. It is also an equation that represents a straight line on a graph. As we proceed further, we are introduced to quadratic equations. The quadratic equations are the ones where the highest power of the variable is two and has two roots. The general form of a quadratic equation is given by; ax2 + bx + c = 0 It is an equation that represents a curved line on a graph. There are different methods to find the roots of a quadratic equation The first method to find the roots of a quadratic equation is the middle-term break. ax2 + sx + tx + c = 0. Here; s × t = a and s ± t = b. The second method is the completing-the-squares method and the most commonly used method is the quadratic formula; (-b ± √(b2- 4ac)) / 2a | When it comes to quadratics and the core curriculum, these types of questions are showing up less and less.
- Completing the Square in a Quadratic Expression - You will learn all the different approaches you can take with these. We start with the more traditional approach and then we expand it. W show you a few helpful tricks that can help you solve these quicker and more accurately.
- Constructing Linear, Quadratic, and Exponential Models of Data - This section of worksheets shows you how to bring your data to life to allow for greater levels of interpretation. This will make the data easier to spot trends in and analyze as a whole.
- Finding and Using the Discriminant - This section shows you how to find the part of the formula that is located under the square symbol. We show you different ways to use this information and it is done in a very practical manner.
- Graphing Linear and Quadratic Functions - These are unique graphs we show you how to visualize them. Most students are used to linear graphs, but quadratic functions are often new to them on a graph. I have seen this taught several different ways; we stay focused on the task with students.
- Quadratic Equations: Completing the Square - We learn a method to solve quadratics by transforming the equation in a manner so that the left side is a perfect square trinomial. Often this is the most focused approach for this skill.
- Quadratics: Using Square Roots and Zero Property - We show you two well known methods for solving these problems much faster. You can work with this several different approaches.
- Solving Quadratic Equations - Basically, what this section is all about. Our worksheets and lessons will work you through how to organize these and break them down into digestible parts for yourself.
- Solving Quadratic Equations By Factoring - We show you how to determine the multiples that generated the overall form. If you consider the quadratic equation as an expanded form of the factor, it makes it much easier to see. I you key in on finding that common factor, it goes by pretty quickly.
- Using the Quadratic Formula - This formula is used to solve and make sense of quadratics. As long as the equation is in the form (ax2 + bx + c), this formula can be used.
- Working With Simplified Quadratic Equations - We show you how to manipulate them to your advantage. They are usually found in their lowest form, but make sure to check them. They make be a few factors from there.
Methods for Solving Quadratic Equations
There are four common methods used to solve quadratics (ax2 + bx + c = 0. We can use them at different times that make them advantageous to use over the other methods.
Factoring - Most students will only learn the most common form, which is by factoring, until they reach more advanced levels of math. This is often the fastest and easiest method. When factoring, we start by getting all the terms to one side and get a zero on the other side. From there you factor what is on the non-zero side. You then check your answer by inserting those values into the original equation. This only works for equations that are factorable.
Square Root Property - This is commonly used on equations that follow one of these two forms: ax2 = c or (ax + b) 2 = c. Using this method, you start by isolating the term that contains the squared variable. You then take the square root of both sides to solve for that variable. Since square roots have the possibility of being positive or negative, we must place the ± symbol in front of the side that contains the constant after calculating the square root.
Completing the Square - We can also solve these by completing the square. This is where we rearrange and insert values into the original quadratic nearly into a square. This is done on a case-by-case level. The overall goal is to find where the original value will equal zero. You can always process these calculations, but it can get messy when dealing with many coefficients.
Using the Quadratic formula - Once you have an equation in the standard form, you just plug the known values into the formula. Students will get confused with which variable is which, but it just follows the standard format: ax2 + bx + c , where a is the value in front of the x2, b is the value in front of the x, and c is the just the constant value. Once you identify these values you just plug them into the formula and solve it from there.
The last, of the more common, methods used to solve these equations is just to graph the equation on a coordinate grid. In many cases students can just plug the values into a graphing calculator to visualize the graph. This is often used just to check answers. Since their graph resembles the letter U because they form parabolas, it will pass across the x-axis twice. These x-intercepts tell us the value of you guessed, both x values within the equation.