Questions and Answers
Why is there an interval over which the graph decreases?
C
The table shows some values that satisfy the quadratic equation. Is this statement true or false?
True
What is the vertex of the parabola? Round to the nearest hundredth.
B
What does the vertex (8.33, 236.67) represent in context?
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What are the zeroes of the function? Round to the nearest hundredth.
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What do the zeroes mean in context?
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To earn a daily profit of $150 from the sale of soccer balls, what price should the store charge for each soccer ball?
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How to find the price per football needed to meet the profit goal of $400?
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What do the intersection points of the graphs represent?
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Study Notes
Profit Model for Soccer Balls
- Daily profit for selling soccer balls is modeled by the quadratic equation y = -6x² + 100x - 180.
- The graph of this equation decreases at certain intervals due to the nature of the parabola opening downwards.
Vertex of the Parabola
- The vertex is at (8.33, 236.67), representing the maximum daily profit of $236.67.
- This maximum occurs when soccer balls are priced at $8.33 each.
Zeroes of the Function
- Zeroes of the quadratic equation indicate the price points where profit equals zero.
- Identifying the zeroes can help determine break-even prices for selling soccer balls.
Achieving Specific Profit Goals
- To achieve a daily profit of $150, solve the equation 150 = -6x² + 100x - 180.
- The solutions x = 4.53 and x = 12.13 indicate that pricing soccer balls at these values yields the desired profit.
Profit from Football Sales
- With soccer balls priced at $7.50, the store earns $232.50 in daily profit.
- To meet a total profit goal of $400, additional profit of $167.50 must come from football sales.
- The relevant equation for football profit is 167.50 = -4x² + 80x - 150, leading to potential football prices of $5.46 and $14.54.
Intersection of Profit Graphs
- Two quadratic equations model profits for soccer balls and footballs respectively.
- Intersection points show when the price and profit for each type of ball are equal.
- Key intersection points are approximately (8.16, 236.49) and (1.84, -16.49):
- At $8.16, the store makes equal profit (~$236.49) from both balls.
- Pricing at $1.84 results in no profit for either type.
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Description
These flashcards focus on understanding quadratic equations in the context of real-world applications, such as profit modeling in a sporting goods store. Each card presents scenarios and questions that test your grasp of the concepts related to quadratic functions.
