Quadratic Equation Word Problems

Many students find quadratic equations word problems difficult. At TuLyn, we created word problems on quadratic equations to help you better understand quadratic equations.

Solving Quadratic Equations Word Problems

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Imaginary Roots Word Problems

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Discriminant Word Problems

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Factoring Quadratic Equations Word Problems

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Are you looking for quadratic equations word problems? TuLyn is the right place. We have tens of word problems on quadratic equations and hundreds on other math topics.

Below is the list of all word problems we have on quadratic equations.

Quadratic Equations Word Problems

  • A ball is shot into the air (#3415)
    A ball is shot into the air. It's height , h in metres after t seconds is modeled by h=-4.9t2 + 30t +1.6...
    solving equations, quadratic equations, solving quadratic equations, equations
  • A balloon is rising from the ground (#457)
    A balloon is rising from the ground at 4 feet per second. Another balloon is at 756 feet and descending at 3 feet per ...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations, equations
  • A framer at a photo gallery (#516)
    A framer at a photo gallery wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye, the area of the matte should equal the area of the print. If the print measures 40 cm by 60 ...
    solving equations, solving quadratic equations, quadratic equations, equations
  • A machine produces open boxes (#3217)
    A machine produces open boxes using square sheets of plastic. The machine cuts equal sized squares measuring 2 inches on a side from each corner of the sheet, and then shapes the plastic into an open box by turning up th esides. If each box must have a volume of 242 cubic inches, find the length of one side of the open ...
    quadratic equations, equations
  • A model rocket is shot into the air (#3116)
    A model rocket is shot into the air and its path is approximated by h = -5t2 + 30t where h is the height of the rocket above the ground in metres and t is the elapsed time in ...
    solving quadratic equations, quadratic equations, solving equations, equations
  • A motor boat travels (#2261)
    A motor boat travels 400km. If the boat went 18km/h faster, it could have traveled 600 km in the same amount of ...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • A parallelogram has a base (#2178)
    A parallelogram has a base of length 2x +1 and a height of x+3 and has an area of 42 square units. Find the base and height of the parallelogram. (A=BH)
    solving quadratic equations, quadratic equations, solving equations, equations
  • A rectangle corral is to be built (#2014)
    A rectangle corral is to be built using 70m of fencing. If the fencing has to enclose all four sides of the ...
    solving equations, quadratic equations, equations, solving quadratic equations, completing the square
  • Ahmed has first half of a treasure map (#1104)
    Ahmed has first half of a treasure map, which indicates that the treasure is buried in the desert (2x + 6) paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must go to the Castle Rock, walk x paces to the North, and then walk (2x + 4) paces to the East. If they share their information, then they can find x and save a lot of ...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • At a point 30 meters from the base of the tower (#3524)
    At a point 30 meters from the base of the tower, the distance to the top of the tower is 2 meters more than twice the height of the ...
    equations, quadratic equations
  • completing the square (#505)
    The path of the ball for many golf shots can be modeled by a quadratic function. The path of a golf ball hit at an angle of about 10 degrees to the horizontal can be modeled by the function, h= -0.002d2 + 0.4d, where h is the height of the ball, in meters, and d is the horizontal distance the ball travels, in meters, until it first hits the ground.
    a) What is the maximum height reached by the ball?
    b) What is the horizontal distance of the ball from the golfer when the ball reaches its maximum ...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • completing the square (#737)
    change to vertex-axis form by completing the square
    f(x)=x2+4x-5
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • Completing The Square (#3562)
    i want to change the carpet in an office that measure 12 feet by 15 feet, if the carpet cost $12...
    quadratic equations, solving equations, equations, solving quadratic equations, completing the square
  • Completing The Square (#5651)
    suppose that an open box is to be made from a square sheet of cardboard by cutting out 4-inch squares from each corner  and then folding along the bottom of the ...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • Completing The Square (#6880)
    each pail of plaster covers 81 square feet of ...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • Completing The Square (#7366)
    Ahmed has the first half of a treasure map, which inducastes that the treasure is buried in the desert (2x+4) paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must go to Castle Rock, walk 'x' paces to the North, and then walk (2x+4) paces to the East. If they share their information, then they can find 'x' and save a lot of ...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • Completing The Square (#7790)
    Five times the square of a number is 980...
    completing the square, solving quadratic equations, quadratic equations, quadratic equations, solving equations, equations
  • Completing The Square (#7790)
    Five times the square of a number is 980...
    completing the square, solving quadratic equations, quadratic equations, quadratic equations, solving equations, equations
  • Completing The Square (#7988)
    find the minimum product of two numbers whose difference is 9
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • Completing The Square (#10988)
    Ball drops from 70 meter bridge.  What is height of ball to the nearest tenth of a meter exactly 2 seconds after ball is ...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • Completing The Square (#10989)
    Ball drops from 70 meter bridge.  What is height of ball to the nearest tenth of a meter exactly 2 seconds after ball is ...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • Frank`s Specialty Coffees makes (#1030)
    Frank's Specialty Coffees makes a house blend from two types of coffee beans, one selling for $9.05 per pound, and the other selling for $6.25 per pound.  His house blend sells for $7.37 per pound.  If he is using 9lb of the 6.25/lb beans, how many pounds of the $9...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • How do the Quarter Pounder and Whopper (#422)
    How do the Quarter Pounder and Whopper with cheese measure up in the calorie department? Actually, not too well. Two Quarter Pounders and three whoppers with cheese provide 2607 calories. Even with one of each provides enough calories to bring tears to Jenny Crag's eyes-9 calories in excess of what is allowed on a 1000 calories-a-day ...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • One positive integer is 8 less (#816)
    One positive integer is 8 less than twice another and the sum of their squares is 244
    equations, systems of equations, solving quadratic equations, solving systems of equations, quadratic equations, solving equations, systems
  • Quadratic Equations (#3636)
    If f(x) equals X to the fourth power minus x plus 2...
    equations, quadratic equations
  • Quadratic Equations (#5114)
    A boat travels 12 km upstream and back in 1 hour 45 minutes. If the speed of the current is 3 km/h ...
    equations, quadratic equations
  • Quadratic Equations (#3902)
    a rectangular box is to be built with a 15 by 12 ft. piece of material by cutting square corners, if the volume of the box is 176 cubic ft. find the dimensions of the square corners
    quadratic equations, equations
  • Quadratic Equations (#3966)
    A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 ...
    quadratic equations, equations
  • Quadratic Equations (#4183)
    An open rectangular gutter is made by turning up the sides of a piece of metal 20 inches wide. The area of the cross section of the gutter is 50 inches ...
    quadratic equations, equations
  • Quadratic Equations (#4816)
    A square mirror has sides measuring 2 feet less than the sides of a square painting.  If the difference between their areas is 32 square ...
    quadratic equations, equations
  • Quadratic Equations (#4840)
    the sum of two numbers is 10 and the sum of their squares is 58. Find the numbers
    quadratic equations, equations
  • Quadratic Equations (#5013)
    THE perrimeter of a rectangle is 34cm. given that the diagonal is of length 13cm, and that the width is xcm, derive the equation x squared - 17x + 60 = 0...
    quadratic equations, equations
  • Quadratic Equations (#5186)
    the product of two consecutive integers is 156 .  Use the equation n(n+1)=156 to find the integers
    quadratic equations, equations
  • Quadratic Equations (#5233)
    Doy and his son can do a job in 4 and a half days. After they have worked for 3 days, Doy got sick, and the son finished the task in 6 more ...
    quadratic equations, equations
  • Quadratic Equations (#5684)
    the square of a number decreased by 4 times the number equals 21...
    quadratic equations, equations
  • Quadratic Equations (#6564)
    Diagonal brace. The width of a rectangular gate is 2 meters
    (m) larger than its height. The diagonal brace measures
    6 ...
    quadratic equations, equations
  • Quadratic Equations (#6663)
    we have to find the maximum number of pieces for each number of certain slices
    quadratic equations, equations
  • Quadratic Equations (#7198)
    A group of office workers plans to share equally the $100 cost of giving a baby shower for a coworker.  If they can get six more people to share the cost then the cost per person will decrease by $15...
    quadratic equations, equations
  • Quadratic Equations (#7315)
    suppose that an object is 100pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 mile from the center of the earth.)
    quadratic equations, equations
  • Quadratic Equations (#7752)
    the park is twice as long as it is wide.its length is 3...
    quadratic equations, equations
  • Quadratic Equations (#9118)
    the length of a rectangle is 6 inches more than it is wide. The area of the rectangle is 91 square ...
    quadratic equations, equations
  • Quadratic Equations (#9352)
    A gardner sets 180 plants in rows.  Each row contains the same number of plants.  If there are 40 more plants in each row, the gardner would need 6 fewer ...
    quadratic equations, equations
  • Quadratic Formula (#7779)
    A rectangle is 4/3 as long as it is wide.  A second rectangle is 4 meters longer and 2 meters wider than the first, and its area is twice that of the ...
    quadratic formula, formulas, solving quadratic equations, quadratic equations, solving equations, equations
  • Quadratic Formula (#7780)
    To raise $1,000, the members of the Nice People Club pledged to chip in equal amounts.  However, five of the Nice People did not contribute, so to make the $1,000 the rest of the members had to pay a extra $10 ...
    quadratic formula, formulas, solving quadratic equations, quadratic equations, solving equations, equations
  • Quadratic Formula (#8771)
    A social club charters a bus to go to Six Flags at a cost of $900. At the last minute, 5people decide not to go. This raises the cost per person by $2 each. If the cost is split evenly between all the people who go, how many people originally intended to take the ...
    quadratic formula, formulas, solving quadratic equations, quadratic equations, solving equations, equations
  • Sam takes 6 days less than the number of days (#2982)
    Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 ...
    quadratic equations, equations, work rate, rate
  • Solving Quadratic Equations (#5877)
    A number of students rented a car for $160 for a one weekend trip. if another sudent had joined the original group, each person's share of expenses would have been reduced by $8...
    solving quadratic equations, quadratic equations, solving equations, equations
  • Solving Quadratic Equations (#6691)
    the difference of two integers is 4 and the sum of their reciprocals 4/15...
    solving quadratic equations, quadratic equations, solving equations, equations
  • Solving Quadratic Equations (#7193)
    family received 19 pieces of mail, consisting of magazines, bills, letters, and ads. If the received the same number of magazines as letters, three more bills than letters, and five more ads than ...
    solving quadratic equations, quadratic equations, solving equations, equations
  • Solving Quadratic Equations (#7376)
    a tugboat can travel 8 mph in still water.going against a current it spends 1 hour and 20 minutes more than going the same distance of 8 miles with the ...
    solving quadratic equations, quadratic equations, solving equations, equations
  • Solving Quadratic Equations (#7748)
    if a number is added to its square the result is 42...
    solving quadratic equations, quadratic equations, solving equations, equations
  • Solving Quadratic Equations (#10617)
    A rectangle has a perimeter of 30 inches. The length is twice as long as the ...
    solving quadratic equations, quadratic equations, solving equations, equations
  • Solving Quadratic Equations (#10900)
    A piece of cardboard is twice as long as it iss wide. It is to be made into a box with an open top by cutting 2-inch squares from each corner and folding up the sides. Determine a function V that represents the volume of the ...
    solving quadratic equations, quadratic equations, solving equations, equations
  • Substitution Method (#4406)
    There are 3 times as many houses available with floor plan 2 than there are with floor plan 1. There are 56 houses in total that are ...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • Substitution Method (#6836)
    in the us house of representatives there are 435 members.  if an appropriations bill passes the house with 85 more members voting in favor than against . how many voter in favor and how many voter against
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • Substitution Method (#7346)
    One canned drink is 15% orange juice; another is 5% orange ...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • Substitution Method (#8082)
    The sum of two positive integers is 80...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • Substitution Method (#8396)
    1. Bob and Sara went to a restaurant last Saturday. Sara remembers that she had a steak and Bob remembers that he had a burger. Their total bill was $22 but they dont remember what the cost for each was. Sara remembers that her meal was twice as much as Bob...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • Substitution Method (#9295)
    a)The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.

    b)The sales representative later indicates that there are 3 times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a.

    c)Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.

    d)What are the intercepts of the equation from part a of this problem? What are the intercepts from part b of this ...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • Substitution Method (#10682)
    A farmer grows only sunflowers and flax on his 240 acre farm. This year he wants to plant 80 more acres of sunflowers than ...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • Suppose you decide to move your garden (#892)
    Suppose you decide to move your garden away from the house, so you have to use 50 feet of fencing for four sides.  The length of the garden must be twice as long as the width.  If the area is now 139 feet ...
    equations, solving equations, quadratic equations, completing the square, solving quadratic equations
  • The difference of a positive number (#3073)
    The difference of a positive number and its square is -30...
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • The height of a batted baseball as a function of time (#3535)
    The height, H metres, of a batted baseball as a function of time, t seconds, since the ball was hit can be modeled by the relation H=-2.1(t-2.4)2+13.
    a) what was the maximum height of the ball?
    b) at what time after it was first hit did the ball reach its maximum height?
    c) how far off the ground was the ball first ...
    equations, solving equations, completing the square, quadratic equations, solving quadratic equations
  • The length of a rectangle is 4 feet longer (#1400)
    The length of a rectangle is 4 feet longer than twice its width. If the area is 96 square ...
    solving quadratic equations, quadratic equations, solving equations, equations
  • The perimeter of Mrs. McCord`s rectangular garden (#734)
    The perimeter of Mrs. McCord's rectangular garden is 100 feet. If the length is 1.5 times longer than the ...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • The sum of two numbers (#264)
    The sum of two numbers is 42. The difference is 14...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • The sum of two numbers (#395)
    The sum of two numbers is 26 and their difference is ...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • The width of a rectangular gate (#1824)
    The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures 6 ...
    equations, quadratic equations
  • What value of c makes (#2990)
    What value of c makes x2-x+c a perfect square?
    completing the square, solving quadratic equations, quadratic equations, solving equations, equations
  • Write a mathematical expression for each number (#3161)
    Write a mathematical expression for each number 1 through 18, using only the number 4 and mathematical symbols. The goal is to use the fewest number of 4s as possible. No other digit can be used.  NOTE: Fours can be combined to create 44, 4.4, 444, 0.4...
    quadratic equations, equations
  • You are selling tickets for a high school basketball game (#1127)
    You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450...
    substitution method, solving quadratic equations, quadratic equations, solving equations, equations
  • You have made a quilt (#522)
    You have made a quilt that is 4 feet by 5 feet. You want to use the remaining 10 square feet as a decorative border of uniform ...
    solving quadratic equations, completing the square, quadratic equations, solving equations, equations
  • You want to build a fence around a square garden (#2917)
    You want to build a fence around a square garden that covers 506.25ft2...
    quadratic equations, equations

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Many students find quadratic equations word problems difficult. At TuLyn, we created word problems on quadratic equations to help you better understand quadratic equations.