Find the equation of the parabola that passes through the points 1. 0,5 2,-3 -1,12 2. 2,0 3,-2 1,-2

1.  The equation of parabola is .

2. The equation of parabola is .

Step-by-step explanation:

1.

Let the equation of parabola be

It is given that the parabola passing through points (0,5), (2,-3) and (-1,12).

The value of c is 5.

The equation must be satisfied by the points (2,-3) and (-1,12).

Divide both sides by 2.

                        .... (1)

                           .... (2)

From (1) and (2), we get

Therefore equation of parabola is .

2.

Let the equation of parabola be

It is given that the parabola passing through points (2,0), (3,-2) and (1,-2).

                     .... (3)

The equation must be satisfied by the points (3,-2) and (1,-2).

                    .... (4)

                           .... (5)

On solving (1), (2) and (3), we get

Therefore equation of parabola is .

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.