Question 54938
Find the least value of {{{ 2x^2-4x+3 }}} 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(ax^2+bx+c)}}}form is{{{highlight(x=-b/2a)}}}.
Your a=2, your b=-4, and your c=3
So the x value of the vertex is:
{{{x=-(-4)/(2*2)}}}
{{{x=4/4}}}
{{{x=1}}}
Substitute that in for x and simplify to find the least value:
{{{2(1)^2-4(1)+3}}}
{{{2(1)-4(1)+3}}}
{{{2-4+3}}}
{{{1}}}
Here's what it looks like graphically, to illustrate my point:
{{{graph(300,200,-10,10,-10,10,2x^2-4x+3)}}}
Happy Calculating!!!