Algebra 2: Quadratics & Polynomials Word Problems Challenge

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

The product of two consecutive integers is 72. What are the integers?

• 6 and 7

• 8 and 9

• 9 and 10

• 7 and 8

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 12 meters per second. Use the quadratic formula to find the time when the ball hits the ground.

• 1.75 seconds

• 2.56 seconds

• 4.20 seconds

• 3.10 seconds

A company produces and sells x units of a product. The revenue R from selling x units is given by R(x) = 50x - x^2. How many units should the company sell to maximize revenue?

• 30

• 20

• 40

• 25

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48, where h is the height in feet and t is the time in seconds. When will the projectile hit the ground?

• 2 seconds

• 3 seconds

• 5 seconds

• 4 seconds

A rectangular pool is 4 meters longer than it is wide. If the perimeter of the pool is 48 meters, what are the dimensions of the pool?

• Width: 6 meters, Length: 10 meters

• Width: 10 meters, Length: 14 meters

• Width: 12 meters, Length: 16 meters

• Width: 8 meters, Length: 12 meters

The sum of the squares of two numbers is 100, and their product is 24. Find the two numbers using the quadratic formula.

• 10 and 10

• 8 and 8

• 6 and 4

• 4√6 and 12

A car's value decreases according to the function V(t) = 20000(0.85)^t, where V is the value in dollars and t is the number of years since purchase. After how many years will the car's value be less than $10,000?

• 4

• 8

• 6

• 10

The area of a triangle is given by the formula A = 1/2 * base * height. If the base is 10 meters and the area is 60 square meters, what is the height of the triangle?

• 8 meters

• 10 meters

• 12 meters

• 15 meters

A quadratic function has roots at x = 2 and x = -3. Write the quadratic equation in standard form and find the vertex of the parabola.

• The quadratic equation is f(x) = x^2 + x - 6 and the vertex is (-1/2, -25/4).

• f(x) = x^2 - x + 6 and the vertex is (1/2, 25/4)

• f(x) = x^2 + 5x + 6 and the vertex is (-5/2, -25/4)

• f(x) = x^2 - 5x - 6 and the vertex is (5/2, -25/4)