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On the x-y coordinate plane there is a parabola, y=x(6-x). Which of th
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22 Jan 2016, 04:36
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MathRevolution wrote:
On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that surround with this parabola and x-axis?
I. (1, 4) II. (3, 6) III. (5, 4)
A. I only B. II only C. III only D. I & II E. I, II &III
Plot the graph of equation y=x(6-x)
Since the graph will be an inverted parabola open downwards (i.e. y will be less than x(6-x) for points to be inside the parabola) therefore any point for which y<x(6-x) with positive value of y will be surrounded by the graph and x-axis (as shown in figure)
All points are surrounded as shown in figure and satisfied by (red highlighted equation). Hence,
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Re: On the x-y coordinate plane there is a parabola, y=x(6-x). Which of th
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10 Apr 2016, 18:51
is there a faster way to solve it??? my approach we have -x^2, so parabola is downwards when x=0, y=0, so (0;0) is a point on the parabola. another point of intersection with x axis is x=6. now.. x=5; y=5 x=4; y=8 x=3; y=9 x=2; y=8 x=1; y=5
everything below is inside the parabola 1. 1;4 - is inside, because 1;5 is on the parabola. 2. 3;6 - is inside, because 3;9 is on the parabola. 3. 5;4 - is inside, because 5;5 is on the parabola.
Re: On the x-y coordinate plane there is a parabola, y=x(6-x). Which of th
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10 Apr 2016, 20:42
1
mvictor wrote:
is there a faster way to solve it??? my approach we have -x^2, so parabola is downwards when x=0, y=0, so (0;0) is a point on the parabola. another point of intersection with x axis is x=6. now.. x=5; y=5 x=4; y=8 x=3; y=9 x=2; y=8 x=1; y=5
everything below is inside the parabola 1. 1;4 - is inside, because 1;5 is on the parabola. 2. 3;6 - is inside, because 3;9 is on the parabola. 3. 5;4 - is inside, because 5;5 is on the parabola.
E
Yes, you know that since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points. We don't even need to draw out the parabola.
Just put the relevant points in y = x(6 - x) x = 1, y = 5 lies on the parabola. So (1, 4) will lie below it. Hence, it will be enclosed by the parabola and x axis. x = 3, y = 9 lies on the parabola. So (3, 6) will lie below it. Hence, it will be enclosed by the parabola and x axis. x = 5, y = 5 lies on the parabola. So (5, 4) will lie below it. Hence, it will be enclosed by the parabola and x axis.
Answer (E)
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Re: On the x-y coordinate plane there is a parabola, y=x(6-x). Which of th
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16 Oct 2018, 01:25
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