Math Algebra Quadratic Problems Key

Algebra 2 CP Quadratic Story Problems Name (Key 4.1-4.4 Worksheet Assignment: A6 Use the following information to determine the value of x. 1. Rectangle Area: 36 Width = x. Length = x + 5 36= x(x+5) X2+5x-36=0 X=-9,4 X=4 (x+9)(x-4)Fo 2. Triangle Area: 42 Base = 2x + 8, Height = x + 3 42-2 (2x+8)(x+3) 42=(x+4xx+3) O= x²+7x-30 (x+10xx-3)-0 x=-10,3 x=3 3. Rectangle Area: 30 Width = x, Length = 3x + 1 30=x(3x+1) 0=3x²+x-30 (3x+10xx-3) X=33 X=3 4. A city's skate park is a rectangle 100 feet long by 50 feet wide. The city wants to triple the area of the skate park by adding the same distance x to the length and the width. Write and solve an equation to find the value of x. What are the new dimensions of the skate park? X 50 3(100-50) = (50+x) (100+x) 2 15000= x²+150+5000 0=x²+150x-10000 (x-50)(x1200) = 0 x=50,-260 X= 50 feet Dimensions: 100 by 150ft. 5. A museum has a café with a rectangular patio. The museum wants to add 464 square feet to the area of the patio by expanding the existing patio as shown. a. Find the area of the existing patio. 20.30 600 feet b. Write and solve an equation. By what distance x should the length and the width of the patio be expanded? X-8 feet 600-464-(20+x)(30+x) 1064= x²+50x+600 X2+50x-464=0 (x-8 (x+58)-0 X-81-58 Dimensions: 28 by 38 feet 6. You have a rectangular stained glass window that measures 2 feet by 1 foot. You have 4 square feet of glass with which to make a border of uniform width around the window. What should the width of the border be? 2 X = Y2 foot Frame Area Total Area 4= (2x+2) (2x+1)-2 4= 4x²+6x+2-2 4x²+6x-4=0 2(2x²+3x-2)=0 2(2x-1)(x+2)=0 Picture Arca x=2,2 Dimensions: 2 by 3 fat 7. You have just planted a rectangular flower bed of red roses. You want to plant a uniform border of yellow roses around the flower bed. Because you bought the same number of red and yellow roses, the areas of the border and flower bed will be equal. What should the width of the border of yellow roses be? Border Area Garden Are a x=2 feet (12+2xx8+2x)-96=96 4x²+40x+96-96-96 4x²+40x-96-0 4(x²+10x-24)=0 4(x+12)(x-2)=0 =x=-12 X=2 Dimensions: 12. feet by 16fect 8. A surfboard shop sells 45 surfboards per month when it charges $500 per surfboard. For each $20 decrease in price, the store selis 5 more surfboards per month. How much should the shop charge per surfboard in order to maximize monthly revenue? What is the maximum monthly revenue? x = Number of $20 price decreases Revenue: (500-20x) (45+5x) Revenue =-100x²+1600x +22500 X=8 price Adjustments Cost: 500-2008) = $340 Max x: A03 1600 21-160) 8 Boards: 45+5(8)= 85 Max Rev 28,900 9. A restaurant sells 30 sandwiches each day at a price of $6 each. For each $.25 decrease in price, 15 more sandwiches are sold per day. How much should the restaurant charge to maximize daily revenue? What is the maximum daily revenue? X= number of 25 decreases Revenue = (300:+15x) (6-.25x) Revenue = -3.75x² +15x +1800 Maxx: AoS-15 2(-3.75) 2 X = 2 prie adjustments. Cost = 6-.25(2)= $5.50 Sandwiches 300+15(2)= 330 Max Rev = $1815