SOLUTION: Please help me with this equation how do I work this out? Consider the function {{{f(x) = x^2 + 4x + 1}}}. Find h, the x-coordinate of the vertex of this parabola.

Algebra ->  Linear-equations -> SOLUTION: Please help me with this equation how do I work this out? Consider the function {{{f(x) = x^2 + 4x + 1}}}. Find h, the x-coordinate of the vertex of this parabola.       Log On


   

Question 179521: Please help me with this equation how do I work this out? Consider the function f%28x%29+=+x%5E2+%2B+4x+%2B+1. Find h, the x-coordinate of the vertex of this parabola.
Found 2 solutions by jim_thompson5910, nerdybill:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: From f%28x%29=x%5E2%2B4x%2B1, we can see that a=1, b=4, and c=1.


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.


x=%28-%284%29%29%2F%282%281%29%29 Plug in a=1 and b=4.


x=%28-4%29%2F%282%29 Multiply 2 and 1 to get 2.


x=-2 Divide.


So the x-coordinate of the vertex is x=-2. Note: this means that the axis of symmetry is also x=-2.


So consequently, h=-2 (since "h" is the x-coordinate of the vertex)

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2+%2B+4x+%2B+1
The axis of symmetry can be found:
-b/2a = -4/2 = -2
.
Therefore, the x-coordinate of the vertex is -2