Atlanta Technical College Quadratic Formula and Equation Solution Problems

Connecting quadratic graphs to analytical solutions and real-world applications to quadratic functions.

Graph and solve the following functions:

1. Suppose you launch a tennis ball off a 5-meter-tall building, and it follows the following trajectory: y=-2x² +6x +5
   How far would the tennis ball travel before hitting the ground?
2. A rocket is launched from rest, at ground level. The graph of the rocket’s velocity with respect to time looks as follows: y= 0.15x²
   How fast is the rocket traveling after 15 seconds?
3. y = x² -2x +2
4. y = 3x² -2x + 2

Insert the graph picture here:

Insert the graph picture here:

Insert the graph picture here:

Insert your analytical solution here:

Insert the graph picture here:

Insert your analytical solution here:

After you answer those questions, I need you to answer the following questions!

• What connections do you see between the graphs of the functions of the functions and the analytical solutions (1-2 sentences)?
• Does every x-intercept correspond to a real-solution in the function?

• Why do some functions seem to have no x-intercepts? What do their solutions look like when solved analytically (2 sentences)?

Which method do you think would have the best real-world applications and why (1-2 sentences)?