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Want to see correct answers? Login or join for free! Looking for Algebra worksheets? Check out our pre-made Algebra worksheets! Filter By Grade You are browsing Grade 9 questions. Previous Page 1 of 10 Next. Solve for x.

When graphing a linear function, there is always a y-intercept and an x-intercept. True False. Grade 9 Quadratic Equations and Expressions. Expand and simplify. Factor the expression. Which equation represents the graph? Find the solution of the following equation. Which equation represents the graph of the parabola? Simplify as much as possible. Which of the following is NOT a quadratic equation?

You need to have at least 5 reputation to vote a question down. Learn How To Earn Badges.Yes, I know it's tough. You've finally mastered factoring and using the quadratic formula and now you are asked to solve more problems!

Except these are even more tough. Now you have to figure out what the problem even means before trying to solve it. I completely understand and here's where I am going to try to help! There are many types of problems that can easily be solved using your knowledge of quadratic equations.

You may come across problems that deal with money and predicted incomes financial or problems that deal with physics such as projectiles. You may also come across construction type problems that deal with area or geometry problems that deal with right triangles. Lucky for you, you can solve the quadratic equations, now you just have to learn how to apply this useful skill.

Find the maximum height attained by the ball. Let's first take a minute to understand this problem and what it means. We know that a ball is being shot from a cannon. So, in your mind, imagine a cannon firing a ball. We know that the ball is going to shoot from the cannon, go into the air, and then fall to the ground.

Now let's talk about what each part of this problem means. In our equation that we are given we must be given the value for the force of gravity coefficient of t 2.

Take a look Now that you have a mental picture of what's happening and you understand the formula given, we can go ahead and solve the problem. Let's not stop here. Let's take this same problem and put a twist on it.

There are many other things that we could find out about this ball! How long did it take for the ball to reach the ground? Now, we've changed the question and we want to know how long did it take the ball to reach the ground. What ground, you may ask. The problem didn't mention anything about a ground. Let's take a look at the picture "in our mind" again. Do you see where the ball must fall to the ground.

The x-axis is our "ground" in this problem. What do we know about points on the x-axis when we are dealing with quadratic equations and parabolas? Yes, the points on the x-axis are our "zeros" or x-intercepts. This means that we must solve the quadratic equation in order to find the x-intercept. Let's do it! Let's solve this equation. I'm thinking that this may not be a factorable equation. Do you agree? So, what's our solution? Hopefully, you agree that we can use the quadratic formula to solve this equation.

The first time doesn't make sense because it's negative. This is the calculation for when the ball was on the ground initially before it was shot.

**How To Solve Word Problems Involving Quadratic Equations and Rational Algebraic Equations**

This actually never really occurred because the ball was shot from the cannon and was never shot from the ground.Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter?

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Problem Solving. Professional Development. Test Preparation.We can follow the steps given below to solve word problems on quadratic equations. Step 1 :. Step 2 :. Solve the quadratic equation obtained using one of the methods given below. Step 3 :. Relate the solution obtained from one of the methods to the statement asked in the question.

Problem 1 :. Solution :. What is the width of the pathway? Problem 3 :. A bus covers a distance of 90 km at a uniform speed. Find the original speed of the bus. If you have any feedback about our math content, please mail us :.

We always appreciate your feedback. You can also visit the following web pages on different stuff in math. Variables and constants. Writing and evaluating expressions. Solving linear equations using elimination method. Solving linear equations using substitution method. Solving linear equations using cross multiplication method. Solving one step equations. Solving quadratic equations by factoring.Problem 1: A rectangular garden has an area of 14 m 2 and a perimeter of 18 meters.

Find the dimensions of the rectangular garden. The figure above shows how to set up the problem. Problem 2: The sum of two numbers is 12 and their product is What are the two numbers?

### Grade 9 Algebra Word Problems

Problem 3: The quadratic equation for the cost in dollars of producing automobile tires is given below where x is the number of tires the company produces. Find the number of tires that will minimize the cost. To solve this problem, we just need 2 important concepts about quadratic equations. First, when we are trying to maximize or minimize, we need to use the formula below that will help us find the x-coordinate of the vertex.

Problem 4: You want to frame a collage of pictures with a 9-ft strip of wood. What dimensions will help you maximize the area? Solve for l and replace l in the formula for the area. Word problems involving quadratic equations.

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Tough Algebra Word Problems. If you can solve these problems with no help, you must be a genius! Real Life Math Skills Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

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Word problems involving quadratic equations Check out these four great word problems involving quadratic equations in this lesson. Homepage Algebra lessons Word problems involving quadratic equations. Recent Articles. Check out some of our top basic mathematics lessons.

Formula for percentage Finding the average Basic math formulas Algebra word problems Types of angles Area of irregular shapes Math problem solver Math skills assessment Compatible numbers Surface area of a cube.Find these numbers.

Within 11 years, the age of Peter will be half the square of the age he was 13 years ago. Calculate the current age of Peter. Calculate the dimensions of the farm. The three sides of a right-angled triangle are proportional to the numbers 3, 4 and 5. A rectangular garden 50 m long and 34 m wide is surrounded by a uniform dirt road. Calculate the dimensions of a rectangle whose diagonal is 75 m, knowing that is similar to a rectangle with sides measuring 36 m 48 m respectively.

Two natural numbers differ by two units and the sum of their squares is What are these numbers? Two taps A and B fill a swimming pool together in two hours.

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Alone, it takes tap A three hours less than B to fill the same pool. How many hours does it take each tap to fill the pool separately? The length of the sides of a right-angled triangle are measured as three consecutive even numbers in cm. Find the values of these sides. A rectangular piece of cardboard is 4 cm longer than wide. A square of 6 cm is cut out in every corner and the rims are folded upwards to create the box.

Find the dimensions of the box. The first faucet takes more than two hours longer to fill the same tank when functioning without the second tap. How long does it take to fill each one separately? Calculate the dimensions of a rectangle whose diagonal is 75 m, knowing that it is similar to a rectangle with sides measuring 36 m 48 m respectively. Time of A 3 hours. Time of B 6 hours. Hypotenuse 10 cm. You can get a Maths tutor near me on Superprof.

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places. Leave this field empty. Quadratic Word Problems. Learn from home The teachers. Emma June 26, In order to learn how to solve quadratic equations by four different methods, please follow this tutorial ; it's detailed and offers plenty of worked examples and practice questions.

In this tutorial, I assume you have already got a good skill in solving quadratic equations as explained in the above tutorial. This tutorial primarily focuses on solving real-world problems involving quadratic equations. If you think you need a bit more practice before dealing with word problems, here is a question generator and a programme to check your answers:.

The following programme is interactive: by clicking on the buttons, you can generate a random equation and its solutions: they are randomly generated - and unlimited in number.

The book covers every single topic in depth and offers plenty of questions to practise. The questions progress well so that students can get a good conceptual understanding of every major topic. A disciplined practice through this book prepares the students for both examinations fully. There is enough coverage on new additions to the syllabus with a significant amount of questions.

The sum of two numbers is 27 and their product is Find the numbers. Let one number be x. The length of a rectangle is 5 cm more than its width and the area is 50cm 2. Find the length, width and the perimeter. Let the width be x. Find x and the area, if the longest side is 5. The product of two numbers is 24 and the mean is 5.

The sum of numbers is 9. The squares of the numbers is These are quadratic simultaneous equations. There are quite a few real life situations that can be modelled by a quadratic function in an accurate way.

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