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 and ran

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 and ran      Log On


   

Question 906422: 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
Found 2 solutions by lwsshak3, MathLover1:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Let f (x) = x^2+4x-7
(a) Find the coordinates of the vertex.
complete the square:
y=x^2+4x-7
y=(x^2+4x+4)-4-7
y=(x+2)^2-11
(x, y) = (-2,-11)
..
(b) The [Either max/min] value of f is
f ( min ) y=-11
..
(c)domain: (-∞,∞)
range:(-11,∞)

Answer by MathLover1(20850) 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%2F2%2A1=-4%2F2=-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+=++%28-2%29%5E2+%2B+4%28-2%29++-++7+
y+=++4+-8++-++7+
y+=+++-4+-++7+
y+=-11+
so, the coordinates of the vertex are:( -2 ,-11)
(b) The [Either max/min] value of f is
the max or min of a parabola is always the vertex
f+%28+-2+%29+=+-11+
(c) Find the domain and range of f
the domain: R (all real numbers)
the range: { y element R : y%3E=-11 }