Enter the equation of the parabola passing through the points (3, 10), (30, −8), (0, 2).

Answer 1

We looking for equation of parabola in standard form y = ax²+ bx+ c. Point (0,2) is point of parabola and because 2 = a•0² + b•0 + c, c = 2;

now y = ax²+ bx +2.

Points (3, 10) and (30, -8) give us system of two equations for a and b.

9a + 3b + 2 = 10,

900a + 30b + 2 = -8.

9a + 3b = 8

900a + 30b = -10

Let multiply first equation by -10 we and adding:

-90a - 30b = -80

900a + 30b = -10

810a = -90

a = -1/9, 9•(-1/9) + 3b = 8, -1 + 3b = 8, 3b = 9, b = 3.

Equatiopn of parabola y = -1/9x² + 3x + 2