Answer:
; minimum
Step-by-step explanation:
Given:
The function is, ![y=x^{2}+2](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%2B2)
The given function represent a parabola and can be expressed in vertex form as:
![y=(x-0)^{2}+2](https://tex.z-dn.net/?f=y%3D%28x-0%29%5E%7B2%7D%2B2)
The vertex form of a parabola is
, where,
is the vertex.
So, the vertex is
.
In order to graph the given parabola, we find some points on it.
Let ![x=-2,y=(-2)^{2}+2=4+2=6](https://tex.z-dn.net/?f=x%3D-2%2Cy%3D%28-2%29%5E%7B2%7D%2B2%3D4%2B2%3D6)
![x=-1,y=(-1)^{2}+2=1+2=3](https://tex.z-dn.net/?f=x%3D-1%2Cy%3D%28-1%29%5E%7B2%7D%2B2%3D1%2B2%3D3)
![x=0,y=(0)^{2}+2=0+2=2](https://tex.z-dn.net/?f=x%3D0%2Cy%3D%280%29%5E%7B2%7D%2B2%3D0%2B2%3D2)
![x=2,y=(2)^{2}+2=4+2=6](https://tex.z-dn.net/?f=x%3D2%2Cy%3D%282%29%5E%7B2%7D%2B2%3D4%2B2%3D6)
![x=1,y=(1)^{2}+2=1+2=3](https://tex.z-dn.net/?f=x%3D1%2Cy%3D%281%29%5E%7B2%7D%2B2%3D1%2B2%3D3)
So, the points are
.
Mark these points on the graph and join them using a smooth curve.
The graph is shown below.
From the graph, we conclude that at the vertex
, it is minimum.
The solution is a pair of numbers ... one for 'x' and one for 'y' ... that
makes the equation a true statement. There are an infinite number
of solutions. If you use the equation to draw a graph, then the graph
of it is a straight line without ends, and <em><u>every point</u></em> on the line is a
solution to the equation.
Here are a few of them:
(In each pair, the first number is 'x', the second number is 'y'.)
(-10,17)
(-9, 14)
(-8, 11)
(-7, 8)
(-6, 5)
(-5, 2)
(-4, -1)
(-3, -4)
(-2, -7)
(-1, -10)
(0, -13)
(1, -16)
(2, -19
(3, -22)
(4, -25)
(5, -28)
The answer to the question
one way because 3 groups each containing 2 people is already 6 students
Answer:
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Step-by-step explanation: