SOLUTION: i should find the vertex of the following: f(x) = x^2+8x+27 do i have to do it as follows? x^2+8x+16-16+27 (x+4)^2+27 a(x-(-8)^2+27 vertex is (-8, 27)? somehow this

Algebra ->  Finance -> SOLUTION: i should find the vertex of the following: f(x) = x^2+8x+27 do i have to do it as follows? x^2+8x+16-16+27 (x+4)^2+27 a(x-(-8)^2+27 vertex is (-8, 27)? somehow this       Log On


   

Question 193063: i should find the vertex of the following: f(x) = x^2+8x+27
do i have to do it as follows?
x^2+8x+16-16+27
(x+4)^2+27
a(x-(-8)^2+27
vertex is (-8, 27)? somehow this seems very wrong to me...
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%2B8x%2B27, we can see that a=1, b=8, and c=27.


x=%28-%288%29%29%2F%282%281%29%29 Plug in a=1 and b=8.


x=%28-8%29%2F%282%29 Multiply 2 and 1 to get 2.


x=-4 Divide.


So the x-coordinate of the vertex is x=-4. Note: this means that the axis of symmetry is also x=-4.


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


y=x%5E2%2B8x%2B27 Start with the given equation.


y=%28-4%29%5E2%2B8%28-4%29%2B27 Plug in x=-4.


y=1%2816%29%2B8%28-4%29%2B27 Square -4 to get 16.


y=16%2B8%28-4%29%2B27 Multiply 1 and 16 to get 16.


y=16-32%2B27 Multiply 8 and -4 to get -32.


y=11 Combine like terms.


So the y-coordinate of the vertex is y=11.


So the vertex is .