Question 139251
Given the function f(x)=2x^2-8x+3, answer the following questions using specific language to explain each step performed.
----------------------------
1.)determine the nature of the roots, using the discriminant.
discriminant = b^2-4ac
d = 8^2-4*2*3 = 64 - 24 = 40 > 0
Since d>0, the function has two unequal Rean Number solutions.
----------------------------------------
2.) solve by using the quadratic formula
x = [8 +- sqrt(40)]/4
x = 2 +- (1/2)sqrt(10)
-------------------------------
3.) graph using vertex roots and direction
Vertex occurs at x=-b/2a = 8/4 = 2
f(2) = 8-16+3 = -5
Vertex: (2,-5)
Direction:Since the coefficient of x^2 is positive, the parabola opens up.
{{{graph(400,300,-10,10,-10,10,2x^2-8x+3)}}}
------------------------
4,)what is the minimum?
y=-5
maximum?
There is no maximum as the parabola opens up.
---------------------------
5.) what is the axis of symmetry? 
The vertical line thru the vertex: x=2
=========================================
Cheers,
Stan H.