Question

Write the equation of a parabola that meets each set of conditions?

The parabola has a vertical axis and passes through points (1, -7), (5, -3) and (7, 4). Solve algebraically only.

 

Answer 1

Step 1:

The points on the parabola are and .

The parabola has vertical axis.

A standard form of parabola having vertical axis is .

The point passes through the parabola.

                Equation (1)

The point passes the parabola.

        Equation (2)

The point passes the parabola.

         Equation (3)

Step 2:

Solve the three linear equations.

Subtract equation (1) from equation (2).

                  Equation (4)

Subtract equation (2) from equation (3).

                  Equation (5)

Subtract equation (5) from equation (4).

Substitute in equation (4).

Substitute and   in equation (1).

Step 3:

Substitute , and in parabola equation.

The equation of the parabola is .

Solution:

The equation of the parabola is .