436 Word Problems on Parabolas Solutions

1) The zeros of the left arch are (0, 0) and (4, 0)
We'll use the zeros form of the rule: f(x) = a (x - x1 )(x - x2 )
f(x) = a x(x - 4) now we find a by substituting the coordinates (7/2, 49/16)
49/16 = a( 7/2)(7/2 - 4) t a = -7/4

measures are in meters.

2) a generator measuring 3 m. wide, 3 m. long and 4 m. high
The arch of the bridge is a parabola with rule of correspondence .

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3)

a) vertex at (3, 14), initial point at (0, 50) -- we'll use standard form
f (t) = a(t - 3)² + 14
t 50 = a(0 - 3)² + 14 t a = 4
f (t) = 4(t - 3)² + 14, t in months, f(t) in dollars,

b) For how many months was the price of the stock less than \$23?
4(t - 3)² + 14 < 23 t (t - 3)² < 9/4 t t = 3 ! 1.5
For 3 months the stock was less than \$23.

c) How much money did Donald lose in the first 3 months?

He lost 100(50 - 14) = \$3600

d) In what month did the stock regain its original value of \$50? September

e) What was Donald's total profit from the sale of his shares a year after purchase?

Set t = 12 months t f(12) = 4(12 - 3)² + 14 -- each share was worth \$338.00 after 12 mos.

The original price was \$50 -- so his profit is 100(338 - 50) = \$28,800

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 a) Find the coordinates of 1) Jaclyn's house: (25, 20) 2) Zack's house: (25, -30) 3) Viv's house: (50, 0) 4) Steve's house: (0, 0)

b) What is the distance across the park from Jaclyn's to Zack's? 50 meters

c) If Viv walks at 15 meters per second (boy, can she move!!),
how long will she take to reach Jaclyn's via the paths crossing the park?
45 meters at 15 m/s = 3 seconds

d) The bushes that form the hedges of the gardens are planted 1.5 meters apart.
How many of these bushes must we plant to complete both hedges?
The hedge between Jaclyn's (25, 20) and Steve's at (0, 0) is

. We should plant (32/1.5) + 1 plants for this hedge = 22 plants
The hedge between Viv's (50, 0) and Zack's at (25, -30) is

We should plant (39/1.5) + 1 plants for this hedge = 27 plants
We will need 49 plants for the hedges.

e) If the bushes cost \$7.95 each, what will it cost to plant the hedges? (49)(\$7.95) = \$389.55

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