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20 14 senior high school entrance examination for mathematics in Sichuan province
Let the parabola y = ax 2+bx+c (a ≠ 0) intersect the X axis at two points (-1, 0) and (3,0),

The intercept on the y axis is -3. Find the values of A, B and C. 。

Two-point substitution equation

0=a-b+c

0=9a+3b+c

The intercept on the y axis is -3.

Y=-3 when x = 0.

-3=c

Substitute into the previous equation.

0=a-b-3

0=9a+3b-3

Then a= 1 b=-2.

∴ a= 1 b=-2 c=-3