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