Question

What is the equation of a parabola that passes through the points (1,6),(-2,27), (2,11)?

Answer 1

The general form of parabola equation is y = ax² + bx + c, where a, b and c are constants.

The parabola passes through the points (1, 6), (- 2, 27) and (2, 11).

Point (1, 6)      --------->    6 =   a +  b + c,   ------>  (1)

Point (- 2, 27) --------->  27 = 4a - 2b + c,  ------>  (2)

Point (2, 11)    --------->  11 = 4a + 2b + c. ------>  (3).

To find the values of a, b and c, the above equations are to be solved by the elimination method..

Solve (1) and (2) to eliminate the c variable  ---->(1) - (2)

       6 =    a +  b + c

(-) 27 = 4a - 2b + c

    ----------------------

    - 21 = - 3a + 3b ----------->(4)

Solve (2) and (3) to eliminate the a and c variables  ---->(2) - (3)

     27 = 4a - 2b + c

(-) 11 = 4a + 2b + c

    ----------------------

    16 = - 4b  ------>   b = - 4

Substitute b = - 4 in (4).

- 21 = - 3a + 3(- 4)

- 21 = - 3a - 12

- 9 = - 3a --------> a = 3.

Substitute b = - 4 and a = 3 in (1).

6 = 3 - 4 + c

6 = - 1 + c

7 = c.

The equation of parabola is y = 3x² - 4x + 7.