Question

已知抛物线y=x²-(k+2)x+9的顶点在坐标轴上,求k的值

Answer 1

y=x²-(k+2)x+(k+2)²/4-(k+2)²/4+9

=[x-(k+2)/2]²-(k+2)²/4+9

若顶点在x轴

则纵坐标是-(k+2)²/4+9=0

(k+2)²=36

k+2=±6

k=-8,k=4

在y轴,则横坐标是0

所以(k+2)/2=0

k=-2

所以k=-8,k=4,k=-2