SOLUTION: Find the vertex and the axis of symmetry for the following graph: {{{f(x)=-x^2+2x+3}}}

Question 131105: Find the vertex and the axis of symmetry for the following graph:

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the vertex, we first need to find the line of symmetry (ie the x-coordinate of the vertex)
To find the line of symmetry, use this formula:

From the equation we can see that a=-1 and b=2

Plug in b=2 and a=-1

Multiply 2 and -1 to get -2

Reduce

So the line of symmetry is

So the x-coordinate of the vertex is . Lets plug this into the equation to find the y-coordinate of the vertex.

Lets evaluate

Start with the given polynomial

Plug in

Raise 1 to the second power to get 1

Multiply 2 by 1 to get 2

Now combine like terms

So the vertex is (1,4)

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Answer:

So the line of symmetry is and the vertex is (1,4)

If we graph, we can visually verify our answer

Graph of with the line of symmetry and the vertex (1,4)

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