In this activity, students interpret a quadratic equation in context. In the associated Algebra 1 lesson, students solve quadratic equations in context using the methods they learned throughout the unit. The work of this activity supports students to interpret the context to set up the equations so their work can focus on solving the equations. When students decide if they will graph by hand or by using technology, they are using appropriate tools strategically (MP5). Students reason abstractly and quantitatively (MP2) when interpreting values in the context of the situation.

The purpose of the discussion is to focus on interpreting the quadratic function in context. Select students to share their solutions. Here are some questions for discussion:

• “How could you find the exact time when the ball hits the ground?” (Solve the equation from the last question using a method like completing the square.)
• “The graph also touches the -axis near the point . What does this point mean for the situation?” (It is meaningless in this situation since the equation only holds for non-negative times after the ball is kicked. In theory, it could mean that the ball was on the ground about -0.8 seconds before being kicked, but we know the ball was on the roof before it was kicked.)

The goal of this activity is to give students another opportunity to analyze a quadratic equation within the context of a situation. In the associated Algebra 1 lesson, students solve quadratic equations in context using the methods they learned throughout the unit. The work of this activity supports students to interpret the context to set up the equations so their work can focus on solving the equations. When students decide if they will graph by hand or by using technology, they are using appropriate tools strategically (MP5). Students reason abstractly and quantitatively (MP2) when interpreting values in the context of the situation.

The purpose of the discussion is to interpret the function in terms of the situation. Select students to share their solutions. Here are some questions for discussion:

• “Andre solves the last equation and finds solutions at and . Do both solutions make sense? Explain your reasoning.” (Yes, they both make sense. The first value is when the ball is 10 feet above the ground while it is going up, then it comes back down again and is at a height of 10 feet above the ground again later.)
• “The point is on the graph. What does this mean in the situation? Does it make sense?” (It means that almost 3.6 seconds after the ball is kicked, it is 5 feet below the ground. It probably does not make sense for the ball to go underground.)