Section 7.2 lecture - the short leg is 5 yards. Exercise 2a...

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Quadratic Applications
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Quadratic Applications Exercise 1a ) Sandy’s bedroom is in the shape of a rectangle that has an area of 120 square feet. The width is two feet less than the length. Find the dimensions of Sandy’s room. 1) Legend: Let x = Length x-2 = width 2) Draw a picture: x x-2 A=120 sq ft 3) Formula: Area = length * width 4) Equation: x(x-2)=120 x 2 -2x-120=0 (x-12)(x+10)=0 (x-12)=0 or (x+10)=0 x=12 or x = -10 Notice: We came up with two answers….how can this be? We don’t really have two answers. We are talking about length, so all our answer must be positive. So we get to eliminate the negative answers. So……. .x=12 Go back to the legend and calculate the width. The length is 12 feet and the width is 10 feet.
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Quadratic Applications 1) Legend: Let x = Long leg x-3 = Short leg 2) Draw a picture: x x-3 A=20 sq yrd 3) Formula: Area = ½ base* height 4) Equation: 1 x(x-3)=20 2 x 2 -3x =20 2 x 2 -3x = 40 (x-8)=0 or (x+5)=0 x=8 or x = -5 Eliminate the negative answer. So……. .x=8 Go back to the legend and calculate the short leg. The long leg is 8 yards and
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Unformatted text preview: the short leg is 5 yards. Exercise 2a ) LaTonyas lawn is in the shape of a right triangle. The area of the lawn is 20 square yards. If the shorter leg o f the triangle is 3 yards less than the longer leg, what are the lengths of the legs of the triangular lawn? x 2 - 3x -40=0 (x-8) (x+5)=0 Quadratic Applications 1) Legend: Let x = short leg x+3 = Long leg 2) Draw a picture: 15 ft x+3 3) Formula: a 2 + b 2 = c 2 4) Equation: x 2 +(x+3) 2 =15 2 x 2 +x 2+ 6x+9=225 2x 2 - 6x - 216 = 0 (x-9)=0 or (x+12)=0 x=9 or x = -12 Eliminate the negative answer. So. .x=9 Go back to the legend and calculate the long leg. The short leg is 9 feet and the long leg is 12 feet. Exercise 3a ) Shays garden is in the shape of a right triangle. The hypotenuse is 15 feet, and the longer leg is 3 feet more than the shorter leg. What are the lengths of the two legs? 2(x 2 - 3x -108)=0 2(x-9) (x+12)=0 x or leg 2 + leg 2 = hypotenuse 2...
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Section 7.2 lecture - the short leg is 5 yards. Exercise 2a...

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