SOLUTION: Find the least value of {{{ 2x^2-4x+3 }}} and the corresponding value of x

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the least value of {{{ 2x^2-4x+3 }}} and the corresponding value of x      Log On


   

Question 54938: Find the least value of +2x%5E2-4x%2B3+ and the corresponding value of x
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Find the least value of +2x%5E2-4x%2B3+ and the corresponding value of x
:
Graphically, this is a parabola and it's least value would correspond to it's vertex.
The formula for finding the x value of the vertex of a parabola written in standard highlight%28ax%5E2%2Bbx%2Bc%29form ishighlight%28x=-b%2F2a%29.
Your a=2, your b=-4, and your c=3
So the x value of the vertex is:
x=-%28-4%29%2F%282%2A2%29
x=4%2F4
x=1
Substitute that in for x and simplify to find the least value:
2%281%29%5E2-4%281%29%2B3
2%281%29-4%281%29%2B3
2-4%2B3
1
Here's what it looks like graphically, to illustrate my point:
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C2x%5E2-4x%2B3%29
Happy Calculating!!!