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Edmentum Integrated Math2 Unit 3 Activity: Quadratic Relationships
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Jen and her friends are designing a robot for a STEM competition. The goal of the competition is to have a robot complete an obstacle course in the least amount of time.
Jen and her friends need to consider the robot’s height and its width at its base. The robot must be short enough and narrow enough to navigate through several arches along the obstacle course. The director of the competition laid out components of the obstacle course on a coordinate plane. Instead of giving the width and maximum height of the arch, the director created an expression based on the location of the arch on the coordinate plane and gave each team this expression to represent the height of the arch, in inches, at any value of x along the arch:
Factor the expression, and use the factors to find the x-intercepts of the quadratic relationship it represents.
Type the correct answer in each box, starting with the intercept with the lower value.
Draw a diagram of the archway modeled by the equation y = -x2 + 5x + 24. Find and label the y-intercept and the x-intercepts on the sketch. Then find and label the width of the archway at its base and the height of the archway at its highest point, assuming the base of the archway is along the x-axis.
After navigating the obstacle course, the team can create a computer simulation of another obstacle course. Jen and her friends decide they would like to include a curved pit in their obstacle course. They want to experiment with the equation and graph of y = x2 to see how adding and multiplying values to the function will affect the parabola.
Use the graphing tool to view the graph of y = x2 and explore possibilities for their curved pit in the questions that follow.
The team first experiments with changing the position of the curved pit. In the computer program, the vertex begins on the origin, and the curve is modeled by the parent quadratic equation, y = x2.
Match each description with the equation that will create that pit.
Next, the team wants to explore how it can change the steepness of the curved pit.
Identify how the graph of each equation compares with the graph of the parent quadratic equation, y = x2.
Drag the equations to the correct location on the chart. Not all equations will be used.
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.
Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that x represents the number of $1 increases in the cost of the buffet.
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.
Which possible buffet prices could Noah could charge and still maintain the restaurant owner’s revenue requirements?
Select the correct prices in the table.
Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.
Jen and her friends need to consider the robot’s height and its width at its base. The robot must be short enough and narrow enough to navigate through several arches along the obstacle course. The director of the competition laid out components of the obstacle course on a coordinate plane. Instead of giving the width and maximum height of the arch, the director created an expression based on the location of the arch on the coordinate plane and gave each team this expression to represent the height of the arch, in inches, at any value of x along the arch:
Factor the expression, and use the factors to find the x-intercepts of the quadratic relationship it represents.
Type the correct answer in each box, starting with the intercept with the lower value.
Draw a diagram of the archway modeled by the equation y = -x2 + 5x + 24. Find and label the y-intercept and the x-intercepts on the sketch. Then find and label the width of the archway at its base and the height of the archway at its highest point, assuming the base of the archway is along the x-axis.
After navigating the obstacle course, the team can create a computer simulation of another obstacle course. Jen and her friends decide they would like to include a curved pit in their obstacle course. They want to experiment with the equation and graph of y = x2 to see how adding and multiplying values to the function will affect the parabola.
Use the graphing tool to view the graph of y = x2 and explore possibilities for their curved pit in the questions that follow.
The team first experiments with changing the position of the curved pit. In the computer program, the vertex begins on the origin, and the curve is modeled by the parent quadratic equation, y = x2.
Match each description with the equation that will create that pit.
Next, the team wants to explore how it can change the steepness of the curved pit.
Identify how the graph of each equation compares with the graph of the parent quadratic equation, y = x2.
Drag the equations to the correct location on the chart. Not all equations will be used.
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.
Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that x represents the number of $1 increases in the cost of the buffet.
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.
Which possible buffet prices could Noah could charge and still maintain the restaurant owner’s revenue requirements?
Select the correct prices in the table.
Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.
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