Posted by ANONYMOUS.... on Tuesday, March 3, 2009 at 2:50pm.
Determine whether the quadratic function has a minimum or maximum value.Then find the coordinates of the minimum or maximum point.
f(x)=2x^24x

ALGEBRA  Reiny, Tuesday, March 3, 2009 at 3:28pm
if you know Calculus, then
f'(x) = 4x  4
= 0 for a max/min
4(x1) = 0
x = 1
then f(1) = 24 = 2
so (1,2) is a min (since the parabola opens upwards)
if you don't know Calculus, use "completing the square" to find the vertex
f(x) = 2[x^2  2x + 1  1 ]
= 2[(x1)^2  1]
= 2(x1)^2  2
so the vertex is (1,2) as above
or
you could use the formula:
the x of the vertex is b/(2a)
= (4)/2(2)
= 1
etc

ALGEBRA  Damon, Tuesday, March 3, 2009 at 3:30pm
y = 2 (x^22x)
dy/dx = 2 (2x2) = extreme at x = 1
d^2y/dx^2 = 4 so that extreme is a minimum
at x = 1
f(1) = 2
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