Michelle And Maggie Research Paper
Michelle and Maggie are at baseball practice. Michelle throws a ball into the air and when it drops to a height of 5ft., she hits the ball. The height of the ball is modeled by the graph below where t = time in seconds and h = height of the ball from the ground.
Maggie is throwing a ball into the air and catching it. The height of
Maggie’s ball is modeled by the function h(t) = –16t2 + 48t + 15.
Part 1. Which ball goes higher in the air, the ball that is hit or the ball that is thrown? Use complete sentences and show all work to explain how you determined the height that each ball reaches.
Part 2. Determine which girl is likely to be standing on a raised platform.
Use complete sentences to explain how you
determine which girl is on the platform and then determine the height of the platform.
Part 3. Which ball is traveling at a faster average rate of change on the way up? Use complete sentences to explain how you determined the interval at which the height of the ball is increasing and the average rate of change. A video game producer is using the quadratic function f(x) = 4 – x2 to model the path of an arrow shot by a game player. The path of the arrow is shown in the graph below. The point (2, 3) represents the top of the castle wall.
If the player moves so that the arrow will clear the wall at the maximum height, what is the new function that the game producer would need to use? Use complete sentences and explain your work.
Create a quadratic equation in standard form that can be factored.
Write your equation in standard form. Use complete sentences to explain the benefits of writing your equation in standard form.
Write your equation in factored form. Use complete sentences to explain the benefits of writing your equation in factored form.
Write your equation in vertex form. Use complete sentences to explain the benefits of writing your equation in vertex form.
Explain how all three forms can be used together to help you graph a quadratic function. Graph your function and label the y-intercept, the x-intercepts, and the vertex.
Maggie is throwing a ball into the air and catching it. The height of
Maggie’s ball is modeled by the function h(t) = –16t2 + 48t + 15.
Part 1. Which ball goes higher in the air, the ball that is hit or the ball that is thrown? Use complete sentences and show all work to explain how you determined the height that each ball reaches.
Part 2. Determine which girl is likely to be standing on a raised platform.
Use complete sentences to explain how you
determine which girl is on the platform and then determine the height of the platform.
Part 3. Which ball is traveling at a faster average rate of change on the way up? Use complete sentences to explain how you determined the interval at which the height of the ball is increasing and the average rate of change. A video game producer is using the quadratic function f(x) = 4 – x2 to model the path of an arrow shot by a game player. The path of the arrow is shown in the graph below. The point (2, 3) represents the top of the castle wall.
If the player moves so that the arrow will clear the wall at the maximum height, what is the new function that the game producer would need to use? Use complete sentences and explain your work.
Create a quadratic equation in standard form that can be factored.
Write your equation in standard form. Use complete sentences to explain the benefits of writing your equation in standard form.
Write your equation in factored form. Use complete sentences to explain the benefits of writing your equation in factored form.
Write your equation in vertex form. Use complete sentences to explain the benefits of writing your equation in vertex form.
Explain how all three forms can be used together to help you graph a quadratic function. Graph your function and label the y-intercept, the x-intercepts, and the vertex.