?$(1)$?證明：∵判別式?$b^2-4ac=(m-3)^2-4\ \mathrm {m}×(-1)=(m-1)^2+8>0$?
∴不論?$m $?取何值，二次函數(shù)的圖像都與?$x$?軸交于兩點(diǎn)
?$ (2) $?當(dāng)?$m=\frac {9}{2} $?時(shí)，?$y=\frac 92x^2+\frac 32x-1$?
令?$y=0$?，?$\frac 92x^2+\frac 32x-1=0$?
?$x_1=-\frac 23 $?，?$x_2=\frac 13 $?
∴兩個(gè)交點(diǎn)的坐標(biāo)分別是?$(-\frac {2}{3}$?，?$0)$?、?$ (\frac {1}{3}$?，?$0)$?
∴線段?$AB$?的長(zhǎng)為?$1 $?
?$(3) $?由?$(2)$?中拋物線頂點(diǎn)?$P $?的坐標(biāo)為?$(- \frac {1}{6}$?，?$- \frac {9}{8} )$?
∴?$△ABP $?的面積是?$ \frac {1}{2} ×1× \frac {9}{8}=\frac {9}{16}$?
