During a long space mission, Nova and Luna noticed that the station's solar array was producing too little power. The control system modeled its output with P(x) = -2(x - 3)^2 + 98, where x represented the array's orientation setting and P represented power in kilowatts. To understand the pattern, they graphed the function for settings from 0 to 6. Luna recognized a downward-opening parabola with a maximum at (3, 98). Nova calculated that settings 1 and 5 each produced 90 kilowatts, while settings 0 and 6 produced only 80 kilowatts. The station needed at least 92 kilowatts for normal operation, so their current setting of 6 was insufficient. Using the graph, they saw that moving the array toward x = 3 increased the output. They selected setting 3, and the power level rose to 98 kilowatts, safely restoring the station's systems.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
For a downward-opening parabola, consider what the vertex represents.
A student claims that setting x = 6 gives the maximum power because 6 is the greatest orientation setting on the graph. Which statement best explains why the claim is incorrect?
The greatest x-value always gives the smallest value of a quadratic function.The parabola opens downward and has its vertex at (3, 98), so the maximum power occurs at x = 3.The parabola opens upward, so its maximum must occur at x = 0.The power is the same at every setting from x = 0 to x = 6.
Correct! The vertex gives the maximum power because the parabola opens downward.
Not quite. Use the direction the parabola opens and the location of its vertex to identify the maximum.
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Hint
Find the difference between the power at the new setting and the power at the current setting.
The station is currently at setting x = 6, where the array produces 80 kilowatts. Nova moves it to the maximum-power setting x = 3, where it produces 98 kilowatts. By how many kilowatts does the power output increase?
Correct! Moving from setting 6 to setting 3 increases the output by 18 kilowatts.
Try again. Subtract the 80-kilowatt output from the 98-kilowatt output.
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Hint
Use the function to check settings near the vertex. Remember that settings 1 and 5 produce only 90 kilowatts.
The station needs at least 92 kilowatts for normal operation. Which statement about the integer settings 0 through 6 is correct for P(x) = -2(x - 3)^2 + 98?
Only settings 2, 3, and 4 provide at least 92 kilowatts.Only settings 1, 3, and 5 provide at least 92 kilowatts.Settings 1, 2, 3, 4, and 5 all provide at least 92 kilowatts.All integer settings from 0 through 6 provide at least 92 kilowatts.
Correct! Settings 2 and 4 produce 96 kilowatts, and setting 3 produces 98 kilowatts.
Not quite. Check which integer settings give an output of 92 kilowatts or more.
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Güneş Paneli Güç Eğrisi
TR
ARC_G10_PA_02_STORY_03
Güneş Paneli Güç Eğrisi
The Solar Array Power Curve
EN
ARC_G10_PA_02_STORY_03
The Solar Array Power Curve