Question

Please ensure that you provide the important points (the x and y - intercepts, and the vertices),and please clearly label them on the Cartesian coordinate system. [15 points]

Answer 1

Given the piece-wise function

$k(x)=\begin{cases}|x|,x\ge3 \\ \\ 2x^2-4x+3,x<3\end{cases}$

The graph of

$|x|\text{ for x }\ge3$

Is shown below

The graph of

$2x^2-4x+3\text{ for x < 3}$

Is shown below

The graph of the piece-wise function is shown below

The blue curve represents the quadratic function and the red line represent the absolute function