Question

Instructions: State the vertex, axis of symmetry and -intercept for the function. State whether the vertex is a minimum or maximum.

Answer 1

Chemistry => Atomic Structure => Neutron

Neutrons are particles within the atom located in the nucleus, these particles have no charge.

In the image we can identify them as the spheres without writing in the center of the atom, as we will see in the following figure:

Therefore, if we count the amount we will see that there are 4 neutrons inside the nucleus.

Answer: There are 0 neutrons in this lithium around, the neutrons are inside the nucleus and there are 4 neutrons

`y=x^2+2x+3`

Required:

To find the axis of symmetry, vertex, y-intercept and the maximum/,minimum of the given function.

Step-by-step explanation:

Axis of symmetry:

`x=-(b)/(2a)`

From the given equation

`\begin{gathered} a=1 \\ b=2 \end{gathered}`

Therefore,

`\begin{gathered} x=-(2)/(2(1)) \\ \\ x=-1 \end{gathered}`

Vertex:

The axis of symmetry is x=-1,

Now

`\begin{gathered} y=(-1)^2+2(-1)+3 \\ =1-2+3 \\ \\ =2 \end{gathered}`

Therefore, the vertex is

`(-1,2)`

y-intercept:

Set x=0 in to the given equation, we get

`\begin{gathered} y=0+2(0)+3 \\ =3 \end{gathered}`

Therefore, y-intercept is

`(0,3)`

Minimum/maximum:

Now

`(dy)/(dx)=2x+2`
`\begin{gathered} 2x+2=0 \\ 2x=-2 \\ x=-1 \end{gathered}`

Therefore the function is maximum.

Final Answer:

Axis of symmetry : x=-1

Vertex : (-1,2)

y-intercept : (0,3)

The function is maximum.