SOLUTION: Consider the function f(x)=x^2+6x-2. a) Find h, the x-coordinate of the vertex of this parabola.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Consider the function f(x)=x^2+6x-2. a) Find h, the x-coordinate of the vertex of this parabola.       Log On


   

Question 115515: Consider the function f(x)=x^2+6x-2.
a) Find h, the x-coordinate of the vertex of this parabola.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
To find h, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)
To find the axis of symmetry, use this formula:

x=-b%2F%282a%29

From the equation y=x%5E2%2B6x-2 we can see that a=1 and b=6

x=%28-6%29%2F%282%2A1%29 Plug in b=6 and a=1


x=%28-6%29%2F2 Multiply 2 and 1 to get 2



x=-3 Reduce


So the axis of symmetry is x=-3 which means h=-3


Lets evaluate f%28-3%29

f%28x%29=x%5E2%2B6x-2 Start with the given polynomial


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


f%28-3%29=%289%29%2B6%28-3%29-2 Raise -3 to the second power to get 9


f%28-3%29=%289%29%2B-18-2 Multiply 6 by -3 to get -18


f%28-3%29=-11 Now combine like terms


So the vertex is (-3,-11)