Linear and Quadratic Functions: Determining a Quadratic Function

think icon Think & Click: Real World Applications of Quadratic Functions

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Find two consecutive even integers whose product is 14,160.
 
n times the quantity n plus two equals fourteen thousand, one hundred sixty; n squared plus two n equals fourteen thousand, one hundred sixty; n squared plus two n minus fourteen thousand, one hundred sixty equals zero; quantity n plus one hundred twenty times the quantity n minus one hundred eighteen equals zero; n equals negative one hundred twenty or n equals one hundred eighteen
 
Throw out the negative value. If the first even integer is 118 then the next must be 120.
 
You have a garden in your backyard that is 10 yards by 14 yards. You want to build an irrigation ditch around the whole garden that has a uniform width. What is the width of the irrigation ditch if the area increases to 180 yd2?
 

Garden with dimensions 10 yd by 14 yd with a uniform irrigation ditch around the garden.

Write the quadratic formula for this situation.
(2w + 10)(2w + 14) = 180

Multiply the binomials.
4w2 + 48w + 140 = 180

Subtract 180 from both sides.
4w2 + 48w – 40 = 0

Use the Quadratic Formula to Solve for w.
w = .78 or w = -12.78.

Throw out the negative solution.

w = .78 yd
 

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