Best Quadratic Word Problems Worksheet for Practice
If you’re anything like me, you may have noticed how often quadratic equations appear in everyday situations. That’s kind of a strange thing to think about, but it’s true!
Because of the force of gravity on Earth, quadratic relations exist literally all around us. Try it! Pick something up and toss it up into the air and watch as it falls back to the ground. The object’s height over time can be modelled using a quadratic function!
And it doesn’t stop there! Whether you’re calculating how high a ball will fly, how big a garden should be, or unraveling a tricky number riddle, you’re solving real-life word problems using quadratic equations.
As an online teacher myself, I have found it challenging to help my students connect math to the real-world at times. That’s why I created a versatile quadratic word problems worksheet that’s perfect for both classroom and distance learning settings.
This worksheet helps students decode math scenarios in the real-world so that they can practice choosing the right strategy, whether it’s factoring, using the quadratic formula, or applying the vertex equation.
Grab the worksheet below in PDF format to get started right now!
3 Strategies for Solving Quadratic Word Problems
But first, before you start solving, let’s take a moment to review the three key strategies that are often used to solve quadratic word problems.
When my students encounter a quadratic equation, one of the first questions that they ask is “how do I know what to do?”. Most quadratic equations look the same, so it can be difficult to narrow down which strategy to use while mastering the strategies themselves.
The worksheet below will help you build confidence by providing examples that require each of these three classic solution methods, each with real-world context.
Strategy #1: Solving Quadratic Word Problems By Factoring
Factoring is a go-to method when the numbers are clean and the equation is factorable. When you have practiced it, it’s a fast and easy way to find the \(x\)-intercepts of a quadratic equation.
And the \(x\)-intercepts are usually very important in word problems. They often represent time, distance, or other important real-world quantities.
You can check out my walkthrough of how to factor a trinomial, and use my trinomial factoring calculator to help you if you need a walkthrough of a full solution for a factoring problem.
For now, I’ve included a video below that will explain the factoring process needed to solve the quadratic equations in the worksheet below.
Strategy #2: Solving Quadratic Equations Using The Quadratic Formula
Sometimes the numbers aren’t so nice, or factoring simply doesn’t work. That’s when we turn to the quadratic formula.
The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} \]
This formula allows us to calculate the \(x\) values (the solutions to the equation) for any given quadratic equation (including those that can be factored!). To use the quadratic formula, we simply substitute the values for \(a\), \(b\), and \(c\) and work out the result(s).
The answer to your quadratic formula calculation will be the \(x\)-intercepts and will have real-world meaning depending on the problem you are solving.
If you are finding the quadratic formula difficult to use, check out my quadratic formula calculator for full solution walkthroughs for any quadratic formula calculation!
Strategy #3: Solving Quadratic Word Problems Using Vertex Equation
When a quadratic models a real-world motion, like a ball being thrown in the air, the vertex equation can be used to find another key value: the vertex.
The vertex is the location of the maximum or minimum value of a quadratic relation.
For example, in a scenario with a ball being thrown, the vertex is the location of the maximum height reached by a ball, given its height as a function of time.
To find the \(x\)-coordinate of the vertex, we use the vertex equation:
\[x=-\frac{b}{2a}\]
To use this simple equation, we simply substitute the values of \(a\) and \(b\) and solve for the value of \(x\). From there, we can substitute this \(x\)-value into our function to find the maximum height.
How To Solve Quadratic Word Problems
Solving word problems is something that I see many students struggle with. Throughout my teaching career, I have helped thousands of students solve real-world math problems using proven problem-solving strategies that help them feel confident in their approach.
There are many different strategies for solving math word problems, but I personally recommend the following approach:
- Start with a Positive Math Mindset: Build a growth mindset that views mistakes as opportunities for growth. A positive attitude helps students stay calm, think clearly, and see that word problems use familiar math concepts in real-world scenarios.
- Identify Each Key Piece of Information: Carefully read through the problem and separate relevant information from extraneous details. Identify key words that hint at the required math operations, and highlight or underline important numbers and terms.
- Break the Problem into Easy Steps: Divide the problem into smaller parts and solve them one at a time. This strategy helps make complex problems more manageable and clarifies how different parts relate to each other.
- Start Solving the Problem One Step at a Time: Approach each step methodically, checking for errors before moving on.
- Check Your Answer: Always double-check your work by rereading the problem, verifying that your solution makes sense, and ensuring the answer is in the right format and units.
Reading a math problem is a lot like a scavenger hunt: you look for key phrases and values, determine what’s missing, and choose the best strategy to find the answer. The following worksheet is designed to help students practice this kind of critical reading.
In general:
- If the problem contains easy to work with numbers, try factoring.
- If the problem contains messy numbers or cannot be factored, use the quadratic formula
- If the problem asks for a maximum or minimum, use the vertex equation
Get The Quadratic Word Problems Worksheet
This quadratic word problems worksheet includes 8 real-world scenarios that provide students with practice selecting and applying strategies for solving quadratic word problems. In this worksheet you will find examples that involve:
- Calculating the dimensions of a rectangle
- Solving for the sum of the squares of two numbers
- Finding the maximum height of a projectile
- Using the Pythagorean theorem to solve a problem involving a right triangle
- Working with consecutive integers in a logical number puzzle
You can download the full worksheet in PDF format below!
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