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The restorative power of sleep is graphically approximated by the func 30 Nov 2016, 03:04
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The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18
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E
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The restorative power of sleep is graphically approximated by the func 30 Nov 2016, 04:50
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Bunuel
The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18
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The restorative power is given by \(-x^2 + 16x + 36\).

We want the value of x (number of hours) for which it will become 0.

-x^2 + 16x + 36 = 0
x = 18, -2

After 18 hours, the graph will be negative so there will be no positive restoration value.
Answer (E)
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The restorative power of sleep is graphically approximated by the func 30 Nov 2016, 07:19
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The restorative power is given by the equation -x^{2}+16x+36, which is equal to x^2-16x-36. We are told that the restoration value is in the y-axis, and we want to find out after how much sleep we would not get any restoration for our sleep.
So if y becomes 0, we have x^2-16x-36=0.
or
(x-18)(x+2)=0
Which means that x=18 or x=-2
Since we are counting hours of sleep, the answer cannot be negative, thus x=18 and the answer is E.
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The restorative power of sleep is graphically approximated by the func 16 Jun 2017, 23:50
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Bunuel
The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18
Show more

This question is simple yet has a very subtle trap answer- in order to find the values of x we must factor the equation- if you simply plug in values and solve for 0 you would also find that -2 and 18 equal 0. However, theoretically, you cannot have a negative amount of sleep therefore the answer is simply 18. This is just a matter of reading the question


Thus
"E"
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The restorative power of sleep is graphically approximated by the func 13 Jul 2019, 03:07
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Bunuel
The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

The restorative power is given by \(-x^2 + 16x + 36\).

We want the value of x (number of hours) for which it will become 0.

-x^2 + 16x + 36 = 0
x = 18, -2

After 18 hours, the graph will be negative so there will be no positive restoration value.
Answer (E)
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The quadratic function here opens downwards. After the maxima point the effect of sleep is negative. I think point of maxima is the correct answer. As the question asks when does the restorative duties end and not when does the effect of sleep becomes zero.
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The restorative power of sleep is graphically approximated by the func 15 Jul 2019, 09:59
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Every equation can be represented as a graph on X-Y coordinate plot.
For this problem we do not actually need to plot a graph, but having understanding of where a graph lies on coordinate system help in better understanding.
So before reading the explanation I would suggest to google some simple graph of \(x^2\), \(-x^2\), \(x^2\)+1 , and \(x^2\)+x+1 etc
(You can also copy paste same equation on Google ; see attached graph)

Now from figure i.e. understanding of equation, this is an equation of downwards open parabola. As its parabola it can cut x-axis at two point
When it cuts x-axis its y coordinate will be 0.
So putting value in Y=0
0 = -\(x^2\) + 16x + 36
x = -2 or 18

After both this point 'restorative power' i.e. Y coordinate gets negative. So -2 or 18 is Ans
But Sleep hours practically could not be -2. So correct ans is 18
Option E

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2019-07-15 21_55_28--x^2 + 16x + 36 - Google Search.jpg
2019-07-15 21_55_28--x^2 + 16x + 36 - Google Search.jpg [ 25.74 KiB | Viewed 5868 times ]

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The restorative power of sleep is graphically approximated by the func 24 Sep 2020, 23:16
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Wow, this question got me. Too Late.


Concept: Since the A Coefficient in front of (x)^2 is a (-)Negative Value, the Parabola will Open DOWNWARDS and the Vertex, which occurs at the TOP of the Parabola, will be the Maximum Y Value of the restoration you can get.

The Axis of Symmetry/Vertical X-Line that creates a Mirror Image can be found by finding the X-Coordinate:

X = - (b / 2a) = - (16 / 2(-1) = +8

At X = +8 hours of Sleep you can get the MAXIMUM Y Value of restorative value (actually makes sense from a logical perspective).

However, when the Parabola crosses the X-Axis and starts to head down into Quadrant IV, the Restorative Power will no longer kick in.

The amount of hours, after which, the Y-Value starts to become (-)Negative is given by the (+)Positive X-Intercept of the Parabola.

This can be found by setting the Y-Value = 0 and finding the X-Intercepts.

-(x^2) + 16x + 36 = 0

x^2 - 16x - 36 = 0

(x - 18) (x + 2) = 0

At the (+)Positive X-Intercept of X = 18 hours, the Y Value will STOP Existing (y will = 0) and the Restorative powers of sleep will no longer work.

-Answer E-
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The restorative power of sleep is graphically approximated by the func 06 Apr 2026, 22:05
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