Quadratic Vertex Word Problems
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- Completing the Square: Word Problem In order to reinforce how to use completing the square, let's do a word problem involving this: Al is an avid skateboarder, and is doing a cr…
By Tommy San Miguel, Alex Federspiel, Jonathan Heller
- (Video) Optimization by Math with Mr. Barnes Math with Mr. Barnes shows a common quadratic function word problem: optimization of area problems. The hardest part of these proble…
By Ben Ferrara, Alex Federspiel, Ruiran Xun, Victor Wang
- The quality of Matha's cookies is usually a little bit suspect. If she puts in too much time, she overthinks it and tries to add too many "special" ingredients. Too little time,…
By Tommy San Miguel, Joshua Siktar, Victor Wang, Alex Federspiel
- Anytime you're given a written scenario that involves a U-shaped movement into the air (bungee jumping, skateboarding, throwing a ball, etc.), there's a decent chance you can us…
By Hannah Bonville, Alex Federspiel, Jonathan Heller, Caroline K
Problems 26
- Michelle wants to build a garden with two even sections, one for carrots and one for tomatoes. If Michelle has 363636 yards of fencing, what is the largest area she can have to …
- Ben kicks a soccer ball with an initial velocity of 484848 ft/s off the ground. The function h(t)=−16t2+48th(t) = -16t^2+48th(t)=−16t2+48t gives the height of the ball after ttt…
- Susie wants to plant an orchard with as shaped above, with l≥w.l\geq w.l≥w. She has 100100100 feet of fencing. If she wants to fit as many trees in as possible in the fence, wha…
- If Susie maximizes the area of her orchard like this, what will the final shape look like?
- A cannon fires a cannon ball into the air off of a pirate ship at 969696 ft/sec from a height of 161616 feet above sea level. The function h=−16t2+96t+16h=-16t^2+96t+16h=−16t2+9…
- Dan is 666 feet tall and throws a baseball with an initial velocity of 363636 ft/s from his head level. The function h=−16t2+32t+6h = -16t^2+32t+6h=−16t2+32t+6 gives the height …
- If Tristan's lawn mowing company charges 505050 dollars to mow a lawn, they get 125125125 people to use their services. For every 555 dollar decrease in price, the company expec…
- Professional soccer player Mia Hamm can kick a soccer ball with the initial velocity v0v_{0}v0 of 272727 meters per second! Assuming she kicks the ball directly up from a half …
- Hannah is selling homemade hats. So far, she has been selling the hats at 10\1010 per hat and typically sells 100100100 hats a week. \\ Hannah is a smart entrepreneur and she kn…
- Cassandra is selling cups of lemonade. So far, she has been selling each cup for 1\11 and typically sells 808080 cups a day. \\ Cassandra is a smart entrepreneur and she knows t…
- A cannonball's trajectory on a foreign planet can be modelled by the function h(x)=−5t2+15t+10h(x)=-5t^2+15t+10h(x)=−5t2+15t+10, where the output of the function gives the heigh…
- Where is the bullet?
- How high is the drop? Hint: Can you factor this quadratic function? It might also help to visualize the function.
- Adam and Sarah decided to build model rockets together. While building these rockets together Sarah and Adam decided to have a competition to see who's rocket would fly the high…
- Where is the vertex?
- What is the most amount of tickets sold in any given hour?
- You plan on constructing a sandbox on a playground. You have about 404040 meters of material to create the barrier of the rectangular sandbox. What is the largest area you can c…
- You plan on constructing a sandbox on a playground. You have about 404040 meters of material to create the barrier of the rectangular sandbox. What is the dimension of the box, …
- For rectangles with the same perimeter, is there a general strategy to maximize the area?
- In order to maximize yyy, what should the rental price be?
- In order to maximize profit, yyy, how many shirts should Casey order?
- What is the maximum area of a right triangle with hypotenuse 888? Source: Lexington Math Tournament
- Find all integers aaa such that the polynomial x2+ax+ax^2+ax+ax2+ax+a has integer roots. (Check all that apply). Source: Lexington Math Tournament
- It's time to play golf! Unfortunately for you, it's a windy day and the first hole of the course has a water hazard. You place down your tee and analyze the surroundings, trying…
- It's time to play golf! Unfortunately for you, it's a windy day and the first hole of the course has a water hazard. You place down your tee and analyze the surroundings, trying…
- Let the area-perimeter differential of a square be the square's area minus its perimeter. What is the minimum value of the area-perimeter differential (as a function of the side…