ptsl[m_,p_,x_]:=m (x-p[[1]])+ p[[2]]//Simplify;csp[x_]:=Piecewise[{{-(x-1/2)^2+7/4,x<0},{-(x+1/2)^2+7/4,x≥0}}];

csp[0]

csp[x]

csp[x]//TeXForm

Manipulate[
Show[
Plot[
{csp[x],ptsl[m,{0,1.5},x]
},
{x,-1.5,1.5},
PlotRange->{{-1.5,1.5},{0,3}},
PlotStyle->{Blue,Red},
AspectRatio->1,ImageSize->Small
]
],
{{m,0},-1,1},
SaveDefinitions->True
]