Question

已知抛物线经过点(-1,0)和（3,0）,又与y轴交于（0,-3）,则抛物线的解析式为?

Answer 1

抛物线经过点A(-1,0),B(3,0),二者为抛物线与x轴的交点,二者的横坐标也是y = 0的解.于是抛物线可以表达为y = a(x + 1)(x - 3)

与y轴交于C(0,-3):x = 0,y = a(0 + 1)(0 - 3) = -3

a = 1

y = (x + 1)(x - 3) = x² - 2x - 3