# A quadratic function f is given (a)Express f in standard form (b)Find the vertex and x- and y-intercepts of f. (c)Sketch the graph.(d)Find the domain and range of f.f(x)=x^{2}-2x+3

A quadratic function f is given
(a)Express f in standard form
(b)Find the vertex and x- and y-intercepts of f.
(c)Sketch the graph.
(d)Find the domain and range of f.
$f\left(x\right)={x}^{2}-2x+3$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Yusuf Keller

$f\left(x\right)={x}^{2}-2x+3$The standard form of quadratic equation is $f\left(x\right)=a\left(x-h\right)2+k$
(1)(a)$f\left(x\right)={x}^{2}-2x+1+2.f\left(x\right)=\left(x-1\right)2+2$
On comparing it with equation (1) we get:$h=1$,$k=2\left(b\right)$ The vertex V is given by $V=\left(h,k\right)=\left(1,2\right)$ The y−intercept is given by $x=0$

$f\left(0\right)=3$

So, we have (0,3) as the y−intercept.

Now the x−intercept is given by equating $f\left(x\right)=0$
${x}^{2}-2x+3=0$
${x}^{2}-3x+x-3=0x$
$\left(x-3\right)+1\left(x-3\right)=0$