SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. {{{f(x)=x^2-12x-5}}} The vertex is ___. (Type an ordered p

Algebra ->  Graphs -> SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. {{{f(x)=x^2-12x-5}}} The vertex is ___. (Type an ordered p      Log On


   

Question 395274: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function.
f%28x%29=x%5E2-12x-5
The vertex is ___.
(Type an ordered pair)
The equation for the line of symmetry is x=___.
The maximum/minimum of f(x) is ___.
Is the value, f(6)=-41 a minimum or a maximum?
Graph.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The x-coordinate of the vertex is given by:
x+=+-b%2F2a and here, a = 1 and b = -12,
x+=+-%28-12%29%2F2%281%29
x+=+6 substitute into the given equation to find the y-coordinate of the vertex:
y+=+x%5E2-12x-5
y+=+6%5E2-12%286%29-5
y+=+-41
The vertex is at: (6, -41)
The equation of the line of symmetry is: x = 6
The vertex (6, -41) is a minimum because the parabola opens upwards (positive coefficient of x%5E2).
graph%28400%2C400%2C-5%2C20%2C-45%2C5%2Cx%5E2-12x-5%29