SOLUTION: Identify the vertex, axis of symmetry, maximum or minimum, and domain and range of the functions f(x)=x^2+6x+5 and f(x)=4(x+2)^2-6 How do you do this?

Question 808919: Identify the vertex, axis of symmetry, maximum or minimum, and domain and range of the functions
f(x)=x^2+6x+5
and
f(x)=4(x+2)^2-6
How do you do this?

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Identify the vertex, axis of symmetry, maximum or minimum, and domain and range of the functions.
***
f(x)=x^2+6x+5
complete the square:
y=(x^2+6x+9)-9+5
y=(x+3)^2-4
This is a parabola that opens upward.
Its vertex form of equation:y=A(x-h)^2+k, (h,k)=(x,y) cooordinates of the vertex.
For given parabola:y=(x+3)^2-4
A=1
vertex:(-3,-4)
axis of symmetry: x=-3
Minimum:y=-4
Domain: (-∞,∞)
Range:[-4,∞)
..
f(x)=4(x+2)^2-6
This is a parabola that also opens upward and has the same vertex form of equation.
A=4
vertex:(-2,-6)
axis of symmetry: x=-2
Minimum:y=-6
Domain: (-∞,∞)
Range:[-6,∞)
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