<p> Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 1</p><p>Flight of the Golf Ball</p><p>An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, 2 can be determined by the following equation: h(t) = at +v0t + s0 where v0 represents the initial upward </p><p> velocity [in our example: ft/second] and the s0 represents the initial height.</p><p>The vertical height of a golf ball hit from ground-level as a function of time is given by the equation represents </p><p> h(t) = –16t² + 96t. </p><p>1. Create a table of values for time from 0 to 6 seconds in increments of 0.5 seconds. Use this table to graph the height of the golf ball at a given moment in time.</p><p>Time 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 [seconds] Height [feet]</p><p>2. What is the maximum height reached by the golf ball and when does this happen? Explain how you know.</p><p>3. a. When does the ball hit the ground? </p><p>Explain how you know.</p><p> b. At what other time was the ball on the ground? Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 2</p><p> c. How does the time when the ball reached its maximum height relate to the times when the ball was on the ground?</p><p>4. a. When is the ball at a height of 100 feet? Explain how you know.</p><p> b. When is the ball at a height of 40 feet? Explain how you know.</p><p> c. How does the time when the ball is at the maximum height relate to when the ball is at a height of 100 feet? … 40 feet?</p><p>Flight of the Golf Ball</p><p>5. The flight of another golf ball can be modeled by the following equation: h(t) = –16(t – 3)² + 144</p><p> a. Use the table below to find values for time from 0 to 6 seconds in increments of 0.5 seconds. </p><p>Time 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 [seconds] Height [feet]</p><p> b. Use this table to graph the height of the golf ball at a given moment in time. Graph on the same graph as question #1.</p><p>6. What was the maximum height the golf ball reached on the second graph and when did it happen? Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 3</p><p>7. At what times was the ball on the ground?</p><p>8. Which question [question #6 or #7] did this form of equation provide direct information about? What information did the equation provide?</p><p>9. If you were given the following equation to describe the path of a golf ball, what information would you know without having to actually graph the equation: f(t) = –16(t – 8)2 + 70 ? Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 4</p><p>10. The flight of another golf ball can be modeled by the following equation: h(t) = (–16t)(t – 6). </p><p> a. Use the table below to find values for time from 0 to 6 seconds in increments of 0.5 seconds.</p><p>Time 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 [seconds] Height [feet]</p><p> b. Use the table to graph the height of the golf ball at a given moment in time. Graph on the same graph as questions #1 and #5.</p><p> c. What is the maximum height of the ball? ______</p><p> d. When was the ball on the ground? ______</p><p>11. What information does this third form of quadratic equation provide?</p><p>12. If you were given the following equation to describe the path of a golf ball, what would you know without having to actually graph the equation: –16t(t – 10)? Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 5</p><p>13. If you were given the following equation to describe the path of a projectile [the path is called a parabola], what would you know without having to actually graph the equation: f(t) = (t + 5)(t – 10)?</p><p>Flight of the Golf Ball</p><p>2 The height of a projectile can be modeled by the following equation: h(t) = at +v0t + s0 where v0 represents the initial upward velocity [in our example: ft/second] and the s0 represents the initial height. </p><p> a. If you were given the following equation to describe the path of a projectile, what would you know without having to actually graph the equation h(t) = –16t² + 100t + 20. </p><p> b. What does the 20 represent in this equation? Explain what it means.</p><p> c. What does the term –16t² represent in this equation? [what would happen to the height of the projectile without it?]</p><p>Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 6 Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 7</p><p>Blast Out of Space</p><p>An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, 2 can be determined by the following equation: h(t) = at +v0t + s0 where v0 represents the initial upward </p><p> velocity [in our example: ft/second] and the s0 represents the initial height.</p><p>The vertical height of a toy rocket as it blast off from ground-level as a function of time is given by the equation </p><p> h(t) = –16t² + 80t. </p><p>1. Create a table of values for time from 0 to 5 seconds in increments of 0.5 seconds. Use this table to graph the height of the rocket at a given moment in time.</p><p>Time 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 [seconds] Height [feet]</p><p>2. What is the maximum height reached by the toy rocket and when does this happen? Explain how you know. Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 8</p><p>3. a. When does the rocket hit the ground? </p><p>Explain how you know. Blast Out of Space</p><p> b. At what other time was the rocket on the ground?</p><p> c. How does the time when the rocket reached its maximum height relate to the times when the rocket was on the ground?</p><p>4. a. When is the rocket at a height of 100 feet? Explain how you know.</p><p> b. When is the rocket at a height of 25 feet? Explain how you know.</p><p> c. How are the times you found related to each other and to the maximum height? Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 9 Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 10</p><p>Football Frenzy </p><p>An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, 2 can be determined by the following equation: h(t) = at +v0t + s0 where v0 represents the initial upward </p><p> velocity [in our example: ft/second] and the s0 represents the initial height.</p><p>The vertical height of a football as it is kicked from ground-level as a function of time is given by the equation </p><p> h(t) =–16t² + 72t. </p><p>1. Create a table of values for time from 0 to 4.5 seconds in increments of 0.25 seconds. Use this table to graph the height of the football at a given moment in time.</p><p>Time 0 0.25 0.5 0.75 1.0 1.25 1.5 1..75 2.0 2.25 2.5 2.75 3.0 3.25 3.5 3.75 4.0 4.25 4.5</p><p>Height Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 11</p><p>2. What is the maximum height reached by the football and when does this happen? Explain how you know.</p><p>3. a. When does the football hit the ground? </p><p>Explain how you know.</p><p> b. At what other time was the football on the ground?</p><p> c. How does the time when the football reached its maximum height relate to when the football was on the ground?</p><p>4. a. When is the football at a height of 100 feet? Explain how you know.</p><p> b. When is the football at a height of 20 feet? Explain how you know. Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 12</p><p> c. How are the times you found related to each other and to the maximum height?</p><p>Football Frenzy</p><p>Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 13</p><p>World Cup Soccer</p><p>An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, 2 can be determined by the following equation: h(t) = at +v0t + s0 where v0 represents the initial upward velocity [in our example: ft/second] and the s0 represents the initial height.</p><p>The vertical height of a soccer ball as it is kicked from ground-level as a function of time is given by the equation Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 14</p><p> h(t) = –16t² + 48t. </p><p>1. Create a table of values for time from 0 to 3 seconds in increments of 0.25 seconds. Use this table to graph the height of the soccer ball at a given moment in time.</p><p>Time 0 0.25 0.5 0.75 1.0 1.25 1.5 1..75 2.0 2.25 2.5 2.75 3.0</p><p>Height</p><p>2. What is the maximum height reached by the soccer ball and when does this happen? Explain how you know.</p><p>3. a. When does the soccer ball hit the ground? </p><p>Explain how you know.</p><p> b. When else was the soccer ball on the ground?</p><p> c. How do these two times relate to the time it took for the soccer ball to reach its maximum height?</p><p>4. a. When is the soccer ball at a height of 100 feet? Explain how you know. Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 15</p><p> b. When is the soccer ball at a height of 15 feet? Explain how you know.</p><p> c. How are the times Worldyou found Cup Soccer related to each other and to the maximum height? Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 16 Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 17</p><p>I’d Rather Throw a Ball in the Air by Myself than Do Math</p><p>An object that rises and falls under the influence of gravity is called a projectile. Its height, as it rises and falls, 2 can be determined by the following equation: h(t) = at +v0t + s0 where v0 represents the initial upward </p><p> velocity [in our example: ft/second] and the s0 represents the initial height.</p><p>The vertical height of a ball as it is thrown from ground-level as a function of time is given by the equation </p><p> h(t) = –16t² + 25.6t. </p><p>1. Create a table of values for time from 0 to 1.6 seconds in increments of 0.1 seconds. Use this table to graph the height of the ball at a given moment in time.</p><p>Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6</p><p>Height</p><p>2. What is the maximum height reached by the ball and when does this happen? Explain how you know.</p><p>3. a. When does the ball hit the ground? </p><p>Explain how you know.</p><p> b. When else was the ball on the ground? Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 18</p><p> c. How do these two times relate to the time it took for the ball to reach its maximum height?</p><p>4. a. When is the ball at a height of 6 feet? Explain how you know.</p><p> b. When is the ball at a height of 100 feet? Explain how you know.</p><p>I’d Rather Throw a Ball in the Air by c. How are the Myselftimes you than found Do related Math to each other and to the maximum height? Algebra 2 Exploring Quadratic Graphs Name ______For 7.2 19</p>