AAGAB/AA Name ______
Quadratic Unit Part 1 Review
You must show all work (separate sheet) in order to receive credit. Pay attention to the directions for each section!
Solve using inverse operations. Give exact solutions in simplest form.
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Solve by factoring.
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Solve for x by completing the square. Give exact solutions in simplest form. 6.
Solve using the quadratic formula. Give exact solutions in simplest form.
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Solve using any method. Give exact solutions in simplest form.
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16. A rectangular pen is to be made with 48 feet of fencing with a partition
down the middle as shown. Find the dimensions that will produce the
maximum area. Also find the area.
No fence (wall) dimensions: ______
area: ______
17. A student solved as shown.
a. In words, explain the student’s mistake.
b. Solve the equation correctly.
18. Solve the equation using two methods of your choice.
19. Find the discriminant of the quadratic function and complete the table.
Function / Discriminant / # roots / real or imaginary / rational or irrational / # of x -interceptsFind the roots (zeros) of the quadratic functions.
20. 21.
22. If , then
23. If and for all values of x, what is the value
of ?
24. A picture is in the shape of a square of side 5 cm. It is surrounded by a wooden frame of width x cm, as shown in the diagram below.
The length of the wooden frame is l cm, and the area of the wooden frame is A cm2.
(a) Write an expression for the length l in terms of x.
(b) Write an expression for the area A in terms of x.
(c) If the area of the frame is 24 cm2, find the value of x.
25. Mrs Harvey wants to put a 50 m long fence around her rectangular garden. She only needs to fence in 3 sides because the other side is alongside her house.
The width of the garden is denoted by x, and the length by y.
(a) Write an expression for y in terms of x.
(b) Write an expression for the area, A, of the garden, in terms of x.
(c) If the area is 200 m2, find the dimensions of the garden.