Summative Practice: Quadratic Equations

Last updated over 2 years ago

9 questions

This expansive garden, which sits just to the west of the Palace of Versailles, sprawls across nearly 2,000 acres of land. Much of the landscape is styled as a classic French garden with its signature symmetry and order. The manicured lawns are dotted with flowers, sculptures, and fountains that date back to the time of Louis XIV. Fit for a king, the Gardens of Versailles were named a UNESCO World Heritage Site, along with the palace itself.

PART 1

The garden is roughly in the shape of a rectangle. If you were to find an expression for the area of the garden, what are the variables in this situation?

Write an equation for the area of the garden.

If the length of the garden is 10 times its width, find the dimensions of the garden.

PART 2

The length of the rectangular pool is 750 m and the width is 250 m wide. There is a pathway x ms wide around the pool. Write an expression for the area of the rectangle with the pathway and the pool in it.

If the area of the whole rectangle is 12,500 m^2 more than that of the pool, find the equation of the area of the outer rectangle.

Substitute four values for x in the above equation and explain which value was closest to fulfilling the equation. Using this to predict what the value of x might be.

PART 3

At every corner of the circular pool, there are rectangular gardens if the dimensions of the garden are n+7 and n-3. Find an expression for the total area of all 4 gardens and simplify your answer.

If the total area is 4400 m^2 then find the value of n.

At the very centre, there is a circular pool with a radius of r + 5. If the area of the pool is 2000 m^2 write an equation expressing the area of the pool and solve for r.