Quadradic Equation Word Problems - Examples & Practice
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- (Videos) Solving Geometry Word Problems Using Quadratic Equations by PatrickJMT This video by Patrick JMT covers a quadratic word problem based on area of a rectangle. Summary\l…
By Ben Ferrara, Alex Federspiel, Sarah Walker, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- (Videos) Solve Projectile Problems Using Quadratics by PatrickJMT This video by Patrick JMT works through a word problem based on projectile motion. Summary\large{\text{Summary}…
By Ben Ferrara, Alex Federspiel, Sarah Walker, Amy Feraco, Jonathan Heller, Caroline K
- Quadratic Word Problems Let's look at 222 pretty common types of word problems that use quadratic functions. Recall that quadratic expressions follow this general form: y=ax2+bx…
By Hannah Bonville, Alex Federspiel, Ruiran Xun, Sarah Walker, Jonathan Heller, Anusha Rahman, Caroline K
Problems 47
- If you have 200200200 square feet of wall paper, how large a square wall can you cover? Round the height (or width) to the nearest foot.
- The town of Nowheresville decides to make a pool. The pool is 7 meters by 5 meters. The Town has enough concrete to put a 160 square meter deck around the perimeter as shown abo…
- Donnie's Donut Shop has hired you to make a big flat donut-shaped sign for his store. The donut has to have a hole with a diameter of 444 feet and be even sided the whole way ar…
- If you want the area of the triangle to be 444 square inches and the base has to be 222 inches more than the height, what should hhh be in inches?
- A rectangular box has dimensions 10×x×2x10\times x \times 2x10×x×2x. Given that the volume of the box is 808080, find xxx.
- Three distinct real numbers form (in some order) a 3-term arithmetic sequence, and also form (in possibly a different order) a 3-term geometric sequence. Compute the greatest po…
- An object is launched at 19.619.619.6 meters per second (m/s) from a 58.858.858.8-meter tall platform. The equation for the object's height sss at time ttt seconds after launch …
- The product of two consecutive positive integers is 172217221722. What are the two integers?
- Two positive integers have a product of 153615361536 and are 161616 integers away from each other. What are the two numbers?
- A man has (n+8)(n+8)(n+8) piles of (n−2)(n-2)(n−2) coins each. If he has 875875875 coins, what's nnn?
- Express the number of trees that need to be planted in terms of area used.
- Anna is making a wooden frame for her photo. The photo is 555 by 777 inches. The wooden frame has a width of www. The final area of the photo and frame should be 484848 inches s…
- A Pittsburgh river tour lasts 222 hours. The boat goes 101010 km upstream and then back. The river's current is measured as 1.51.51.5 km per hour. What is the boat's speed?
- The length of a rectangle is 555 more than 333 times the width. Find the dimensions that would give the rectangle an area of 100 ft2100\text{ ft}^2100 ft2.
- Josh bought a pool with a radius of 121212 feet. He wants to increase the pool's radius by rrr feet. The new pool should have an area of 289π ft2289\pi\text{ ft}^2289π ft2. What…
- Tim realizes his car traveled xxx miles to get to work each morning, where x2−12x+35=0x^2-12x+35 = 0x2−12x+35=0. What are the possible distances that Tim lives from work?
- Rachel is trying to change the temperature of her apartment so that it minimizes cost. She figures out the equation to do this is t2+15t+56=0t^2+15t+56=0t2+15t+56=0, where ttt i…
- Steve decides to make a box so he can ship candy to a friend for Halloween. He figures out that the height of the box, hhh inches, satisfies the equation h2−2h−35=0h^2-2h-35 = 0…
- Alex wants to add movies to his collection but given his low budget he can only buy xxx more movies, where 3x2−7x=63x^2-7x=63x2−7x=6. How many more is he able to add to his coll…
- Tony is planning a school field trip and needs to figure out how many buses he should have to drive his class. He figures out the number of buses bbb follows the equation, 2b2=9…
- Julia has a headache. Her three friends, Clark, Linda, and Gabby each give her a different equation to figure out how many pills of ibuprofen to take. Clark says to use xxx pill…
- Sarah is painting a wall at her school. The wall can fit either a smaller number aaa of large flowers or a larger number bbb of small flowers. The numbers a,ba,ba,b are the root…
- April's birthday is in xxx days. She feels like her birthday is 2x2+26x+26=1622x^2+26x+26 = 1622x2+26x+26=162 days away. What is xxx?
- Lauren's math teacher told her class that there would be y=x2+20x−715y=x^2+20x-715y=x2+20x−715 problems on the final test. She said xxx was the amount of problems on the test an…
- A spaceship is traveling around LV-426 to survey it. The navigational computer places the moon's center as the origin. The moon has a diameter of 216021602160 miles and the vert…
- Approximately what is the ratio of viewers that Adam will have to those that Dwayne and Kevin had?
- Her competitor, Paper Jones, knows the equation satisfied by aaa and bbb, but not the exact dimensions. What can Jones say for sure about aaa and bbb?
- When people go sky diving, they are in free fall. This means only the acceleration of gravity is controlling their movement until they release the parachute for a safe landing (…
- How far from the goal was Ibrahimović when he kicked the ball? Give the positive zero of the parabola.
- Assume the ball follows a path of y=−x2+29x+30y = -x^{2}+29x+30y=−x2+29x+30, where xxx represents the horizontal distance between the ball and the blackboard. How far from the b…
- Since the 2018-2019 hockey season started last night, let's incorporate some hockey into this problem. On this play, Adam Henrique flips the puck over Sami Vatanen to give himse…
- A hiker gets lost climbing a mountain by his home. In a fit of anger, he threw his GPS off the cliff (a VERY bad decision). His GPS follows the path of y=−x2+65x+750y = -x^{2}+6…
- The length of a lovely rose garden is 555 feet longer than twice the width. Write an equation representing the area of the garden, AAA, in terms of the width, www.
- This hyper baby goat, also known as a kid, is jumping around and having a great time. Assuming during one of his jumps he follows the path y=4−(x−3)2y = 4 - (x-3)^2y=4−(x−3)2 (i…
- A magical room with dimensions based on user input, uuu, has length, l=4u+9l=4u+9l=4u+9, and width, w=2u+3w=2u+3w=2u+3. Which of the following describes the area of the magical …
- A guitarist finishes a performance with her band and decides to throw her guitar pick out to the audience. Assuming the guitar pick follows the path of y=−x2+13x+30y = -x^{2}+13…
- The University of Pittsburgh has one of the most beautiful campus buildings in the world, The Cathedral of Learning. A select few are able to go onto the roof and see the stunni…
- The Minnesota Vikings quarterback Brett Favre throws an incredible pass to his receiver to win the game in the final seconds of the fourth quarter. If his pass follows the path …
- A backyard has length, l=3x+2l = 3x+2l=3x+2, and width, w=2x−4w = 2x-4w=2x−4. Write an equation in terms of xxx representing the area of the backyard.
- A girl playing with her dog throws a tennis ball for him to fetch. Assuming the ball follows the path of y=−x2+9x+10y = -x^{2}+9x+10y=−x2+9x+10, how far does the ball go? Give t…
- A man launches an air compressed rocket into the air. Assuming the rocket follows the path of y=−x2+146x+600y = -x^{2}+146x+600y=−x2+146x+600, how far does the rocket travel fro…
- An ultimate frisbee player throws a frisbee to her teammate. If the frisbee follows the path of y=−x2+17x+60y = -x^2+17x+60y=−x2+17x+60, how far away should her teammate be in o…
- A fun water park has a cliff jump of height, h=25 feeth = 25 \text{ feet}h=25 feet. Use the equation Δh=v0t+12gt2\Delta h = v_{0}t+\frac{1}{2}gt^{2}Δh=v0t+21gt2 to determine h…
- A cardboard box has length l=3x+7l = 3x+7l=3x+7, width w=2x+3w = 2x+3w=2x+3, and height h=4h=4h=4. Write the equation for the volume VVV of the box with respect to xxx.
- A cat exploring his neighborhood has to jump over a small fence to get to a pond that he suspects may have fish in it. If the cat jumping over the fence follows the path of y=−x…
- A cone has a base radius, r=3x+13r = 3x+13r=3x+13, and height, h=3h = 3h=3. Write the equation for the volume of the cone with respect to xxx. Hint: Volume of a cone is V=13πr2h…
- Peter throws a ball off the top of a building to his friend Michael. The position of the ball is modeled by the equation y=−16t2+60t+40y=-16t^{2}+60t+40y=−16t2+60t+40. Find wher…