SOLUTION: find the vertex, the line of symetry, the minumum/maximum value of the quadratic function and graph. -(x+5)^2-6 vertex= line of symetry= min/max= is it min or max= graph= Th

Algebra ->  Equations -> SOLUTION: find the vertex, the line of symetry, the minumum/maximum value of the quadratic function and graph. -(x+5)^2-6 vertex= line of symetry= min/max= is it min or max= graph= Th      Log On


   

Question 515337: find the vertex, the line of symetry, the minumum/maximum value of the quadratic function and graph. -(x+5)^2-6
vertex=
line of symetry=
min/max=
is it min or max=
graph=
Thank you!
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
-(x+5)^2 -6 = -(x+5)(x+5) -6 = -(x^2 +10x + 25) -6
.
-(x^2 +10x + 25) -6 = -x^2 -10x -25 -6 = -x^2 -10x -31
.
The graph will help orient us to the solution
.
+graph%28500%2C500%2C-12%2C5%2C-12%2C5%2C-x%5E2+-10%2Ax+-31%29+
.
The vertex has a x value of -b/2a = -(-10)/(-2*1) = -5
When x=-5
y = -x^2 -10x -31
y = -25 +50 -31
y = -6
.
The vertex = (-5,-6).
.
The line of symmetry is x=-5, a vertical line.
.
Since the parabola opens 'down' we know the vertex is the maximum.
.
We also know this from the graph.
.
And we can apply calculus to set the first derivative = 0.
dy/dx = -2x -10 = 0
2x = -10
x = -5
Correct.
.
Done.