SOLUTION: I need to find the vertex form/function in form, axis of symmetry and max or min of the following equation, and am really confused. y=x^2+6x+5

Question 180892: I need to find the vertex form/function in form, axis of symmetry and max or min of the following equation, and am really confused.
y=x^2+6x+5
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

In order to find the vertex, we first need to find the x-coordinate of the vertex.

To find the x-coordinate of the vertex, use this formula: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Multiply 2 and to get .

Divide.

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is

.

Now because (which is positive), this means that the parabola opens upward and that there is a minimum.

So the min is the same as the y-coordinate of the vertex. This means that the min is

Here's a graph to confirm our answers:

Graph of
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