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Homework: Completing the Square

Module by: Kenny M. Felder. E-mail the author

Summary: Practice homework set on completing the square.

Exercise 1

A pizza (a perfect circle) has a 3" radius for the real pizza part (the part with cheese). But they advertise it as having an area of 25 ππ size 12{π} {} square inches, because they include the crust. How wide is the crust?

Exercise 2

According to NBA rules, a basketball court must be precisely 94 feet long and 50 feet wide. (That part is true—the rest I’m making up.) I want to build a court, and of course, bleachers around it. The bleachers will be the same depth (*by “depth” I mean the length from the court to the back of the bleachers) on all four sides. I want the total area of the room to be 8,000 square feet. How deep must the bleachers be?

Exercise 3

Recall that the height of a ball thrown up into the air is given by the formula:

h ( t ) = h o + v o t 16 t 2 h ( t ) = h o + v o t 16 t 2 size 12{h \( t \) =h rSub { size 8{o} } +v rSub { size 8{o} } t - "16"t rSup { size 8{2} } } {}

I am standing on the roof of my house, 20 feet up in the air. I throw a ball up with an initial velocity of 64 feet/sec. You are standing on the ground below me, with your hands 4 feet above the ground. The ball travels up, then falls down, and then you catch it. How long did it spend in the air?

Solve by completing the square.

Exercise 4

x 2 + 6x + 8 = 0 x 2 + 6x + 8 = 0 size 12{x rSup { size 8{2} } +6x+8=0} {}

Exercise 5

x 2 10 x + 3 = 5 x 2 10 x + 3 = 5 size 12{x rSup { size 8{2} } - "10"x+3=5} {}

Exercise 6

x 2 + 8x + 20 = 0 x 2 + 8x + 20 = 0 size 12{x rSup { size 8{2} } +8x+"20"=0} {}

Exercise 7

x 2 + x = 0 x 2 + x = 0 size 12{x rSup { size 8{2} } +x=0} {}

Exercise 8

3x 2 18 x + 12 = 0 3x 2 18 x + 12 = 0 size 12{3x rSup { size 8{2} } - "18"x+"12"=0} {}

Exercise 9

Consider the equation x2+4x+4=cx2+4x+4=c size 12{x rSup { size 8{2} } +4x+4=c} {} where cc size 12{c} {} is some constant. For what values of cc size 12{c} {} will this equation have…

  • a. Two real answers?
  • b. One real answer?
  • c. No real answers?

Exercise 10

Solve by completing the square: x2+6x+a=0x2+6x+a=0 size 12{x rSup { size 8{2} } +6x+a=0} {}. (aa size 12{a} {} is a constant.)

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