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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (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: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=x%5E2%2B6x%2B5, we can see that a=1, b=6, and c=5.


x=%28-%286%29%29%2F%282%281%29%29 Plug in a=1 and b=6.


x=%28-6%29%2F%282%29 Multiply 2 and 1 to get 2.


x=-3 Divide.


So the x-coordinate of the vertex is x=-3. Note: this means that the axis of symmetry is also x=-3.


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


f%28-3%29=x%5E2%2B6x%2B5 Start with the given equation.


f%28-3%29=%28-3%29%5E2%2B6%28-3%29%2B5 Plug in x=-3.


f%28-3%29=1%289%29%2B6%28-3%29%2B5 Square -3 to get 9.


f%28-3%29=9%2B6%28-3%29%2B5 Multiply 1 and 9 to get 9.


f%28-3%29=9-18%2B5 Multiply 6 and -3 to get -18.


f%28-3%29=-4 Combine like terms.


So the y-coordinate of the vertex is y=-4.


So the vertex is .


Now because a=1 (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 y=-4


Here's a graph to confirm our answers:


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B6x%2B5%29+ Graph of y=x%5E2%2B6x%2B5