IM Alg1.7.18 Lesson: Applying the Quadratic Formula (Part 2)
Evaluate each expression for , , and
Here are four equations, followed by attempts to solve them using the quadratic formula.Each attempt contains at least one error.
Here are the worked solutions with errors:
Equation 1: Equation 2: Equation 3: Equation 4: Equation 1: Equation 2:
Equation 3:
Equation 4:
The equation represents the height, as a function of time, of a pumpkin that was catapulted up in the air. Height is measured in meters and time is measured in seconds. The pumpkin reached a maximum height of 47 meters. How many seconds after launch did that happen? Show your reasoning.
Suppose someone was unconvinced by your solution. Find another way (besides the steps you already took) to show your solution is correct.
The equation models the revenue a band expects to collect as a function of the price of one concert ticket. Ticket prices and revenues are in dollars. A band member says that a ticket price of either $15.50 or $74.50 would generate approximately $1,000 in revenue. Do you agree? Show your reasoning.
Function is defined by the equation . Its graph opens downward. Find the zeros of function without graphing. Show your reasoning.
Explain or show how the zeros you found can tell us the vertex of the graph of .
Study the expressions that define functions and (which defined the height of the pumpkin). Explain how the maximum of function , once we know it, can tell us the maximum of .