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M ETHOD 2 Using a Graph Another approach is to write a quadratic equation and then use a graph to solve the equation. You can use a graphing calculator to make the graph. P RACTICE STEP 1 Write an equation that models the situation using the height function h 5216t 2 1 h 0 . h 5216t 2 1 h 0 Write height function. 0 5216t 2 1 50 Substitute 0 for h and 50 for h 0 . STEP 2 Enter the function y 5216x 2 1 50 into a graphing calculator. Note that time is now represented by x and height is now represented by y. STEP 3 Graph the height function. Adjust the viewing window so that you can see the point where the graph crosses the positive x-axis. Find the positive x-value for which y 5 0 using the zero feature. The graph shows that y 5 0 when x ø 1.8. c The container hits the ground about 1.8 seconds after it is dropped. SOLVING EQUATIONS Solve the quadratic equation using a table and using a graph. 1. 2x 2 2 12x 1 10 5 0 2. x 2 1 7x 1 12 5 0 3. 9x 2 2 30x 1 25 5 0 4. 7x 2 2 3 5 0 5. x 2 1 3x 2 6 5 0 6. WHAT IF? How long does it take for an egg container to hit the ground when dropped from a height of 100 feet? Find the answer using a table and using a graph. 7. WIND PRESSURE The pressure P (in pounds per square foot) from wind blowing at s miles per hour is given by P 5 0.00256s 2 . What wind speed produces a pressure of 30 lb/ft 2 ? Solve this problem using a table and using a graph. Y1=-16X2+50 Y2= Y3= Y4= Y5= Y6= Y7= Zero X=1.767767 Y=0 8. BIRDS A bird flying at a height of 30 feet carries a shellfish. The bird drops the shellfish to break it and get the food inside. How long does it take for the shellfish to hit the ground? Find the answer using a table and using a graph. 9. DROPPED OBJECT You are dropping a ball from a window 29 feet above the ground to your friend who will catch it 4 feet above the ground. How long is the ball in the air before your friend catches it? Solve this problem using a table and using a graph. 10. REASONING Explain how to use the table feature of a graphing calculator to approximate the solution of the problem on page 272 to the nearest hundredth of a second. Use this procedure to find the approximate solution. Using Alternative Methods 273
Lessons 4.1–4.5 MULTIPLE CHOICE 1. CRAFTS You are creating a metal border of uniform width for a rectangular wall mirror that is 20 inches by 24 inches. You have 416 square inches of metal to use. What is the greatest possible width x of the border? TEKS 2A.8.D A 2 inches B 4 inches C 16 inches D 26 inches 2. PHYSICAL SCIENCE A pinecone falls from a tree branch that is 20 feet above the ground. About how many seconds does it take for the pinecone to hit the ground? TEKS 2A.8.D F 0.80 second G 0.89 second H 1.12 seconds J 1.25 seconds 3. FIREFIGHTING Some harbor police departments have firefighting boats with water cannons. The boats are used to fight fires that occur within the harbor. The function y 520.0035x(x 2 143.9) models the path of water shot by a water cannon where x is the horizontal distance (in feet) and y is the corresponding height (in feet). How far does the water cannon shoot? TEKS 2A.8.A A 12.0 feet B 71.9 feet C 143.9 feet D 287.8 feet �� 274 Chapter 4 Quadratic Functions and Factoring TAKS PRACTICE classzone.com 4. COMPUTERS The diagonal of the screen on a laptop computer measures 15 inches. The ratio of the screen’s width w to its height h is 4:3. What is the height of the laptop screen? TEKS 2A.8.A F 3 inches G 9 inches H 12 inches J 81 inches 5. QUADRATIC FUNCTION Which function’s graph has a vertex of (23, 2)? TEKS 2A.6.B A y 523x 2 2 18x 2 25 B y 52 1 } 2 x 2 1 2x 1 5 C y 5 x 2 1 x 2 6 D y 5 x 2 2 4x 2 25 GRIDDED ANSWER 0 1 2 3 4 5 6 7 8 9 6. PIZZA SHOP A pizza shop sells about 80 slices of pizza each day during lunch when it charges $2 per slice. For each $.25 increase in price, about 5 fewer slices are sold each day during lunch. How much should the pizza shop charge per slice of pizza to maximize revenue? TEKS 2A.8.A 7. VEGETABLE GARDEN You have a rectangular vegetable garden that measures 42 feet by 8 feet. You want to double the area of the garden by expanding the length and width as shown. What is the value of x? TEKS 2A.8.D � ��
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