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Students analyze and draw conclusions about contextual applications using the key features of a function and and its graph. New York State Common Core Math Module 4, Algebra I, Lesson 17 Lesson 17 Summary The standard form of a quadratic function is f(x) = ax2 + bx + c, where a ≠ 0. A general strategy to graphing a quadratic function from the standard form is:
1. Graph the equation f(x) = x2 - 5x + 6 and identify the key features. 2. Graph the equation f(x) = 1/2x2 + 5x + 6 and identify the key features. 3. Paige wants to start a summer lawn-mowing business. She comes up with
the following profit function that relates the total profit to the rate she charges for a lawn-mowing job: Both profit and her rate are measured in dollars. b. According to the function, what is her initial cost (e.g., maintaining the mower, buying gas, advertising)? Explain your answer in the context of this problem. c. Between what two prices does she have to charge to make a profit? d. If she wants to make a profit this summer is this the right business choice?
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