SOLUTION: Let f (x) ={{{ - x^2 + 4x - 7 }}} (a) Find the coordinates of the vertex. (x, y) = ___ (b) The [Either max/min] value of f is f ( __ ) = __ (c) Find the domain an

Algebra ->  Functions -> SOLUTION: Let f (x) ={{{ - x^2 + 4x - 7 }}} (a) Find the coordinates of the vertex. (x, y) = ___ (b) The [Either max/min] value of f is f ( __ ) = __ (c) Find the domain an      Log On


   

Question 906441: Let f (x) =++++-+x%5E2+%2B+4x+-+7++++
(a) Find the coordinates of the vertex.
(x, y) = ___
(b) The [Either max/min] value of f is
f ( __ ) = __
(c) Find the domain and range of f
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Let f+%28x%29+=+-+x%5E2+%2B+4x++-++7+...as you can see, a=-1, b=4, and c=-7
(a) Find the coordinates of the vertex.
x=-b%2F2a is x-coordinate of the vertex
so,
x=-b%2F2a=-4%2F%282%2A-1%29=-4%2F-2=2
and, to find the y-coordinate that goes with it,use that value for x in our equation
f+%28x%29+=+-+x%5E2+%2B+4x++-++7+ ...solve for f%28x%29 which is equal to y
y+=++-%282%29%5E2+%2B+4%282%29++-++7+
y+=++-4+%2B8++-++7+
y+=+++4+-++7+
y+=-3+
so, the coordinates of the vertex are:( 2 ,-3)
(b) The [Either max/min] value of f is
the max or min of a parabola is always the vertex
f+%28+2+%29+=+-3+
(c) Find the domain and range of f
the domain: R (all real numbers)
the range: { y element R : y%3E=-3 }

+graph%28+600%2C+600%2C+-10%2C+10%2C+-15%2C+10%2C+-x%5E2+%2B+4x-7%29+