Question

The number of point of intersection of the curve $y=max\{x^2-3x+2,2\}$ with the $x-$axis is

Answer 1

Given, $y=max\{x^2-3x+2,2\}$
Let $f\left(x\right)=x^2-3x+2$ and $g\left(x\right)=2$
$\Rightarrow x^2-3x+2=2$
$\Rightarrow x=0,3$ (Points of intersection)
To draw the given curve, we have to draw the graph of $f\left(x\right)=x^2-3x+2$ (parabola) and $g\left(x\right)=2$ (horizontal line), Neglecting the graph below the points of intersection.

So, the curve do not intersect the $x-$axis