Given:
[tex]f(x)=2x^2-x+1[/tex][tex]a=2\text{ ; b= -1 ; c=1}[/tex]
Graph opes upwards.
Let the vertex be (h,k)
[tex]h=-\frac{b}{2a}[/tex][tex]h=-\frac{(-1)}{2(2)}[/tex][tex]h=\frac{1}{4}[/tex][tex]k=f(h)[/tex][tex]k=2(\frac{1}{4})^2-\frac{1}{4}+1[/tex][tex]k=2(\frac{1}{16})-\frac{1}{4}+1[/tex][tex]k=\frac{1}{8}-\frac{1}{4}+1[/tex][tex]k=\frac{1-2+8}{8}[/tex][tex]k=\frac{7}{8}[/tex][tex]\text{Vertex}=(\frac{1}{4},\frac{7}{8})[/tex]
Axis of symmetry is
[tex]x=\frac{1}{4}[/tex]
y- intercept
x=0,
y=1
There is no x intercept .
Domain:
[tex](-\infty,\infty)[/tex]
Range:
[tex]\lbrack\frac{1}{4},\infty)[/tex]
The function is increasing:
[tex](\frac{1}{4},\infty)[/tex]
The function is decreasing:
[tex](-\infty,\frac{1}{4})[/tex]
