Question

Find an equation in standard form of the parabola passing through the points (-1, 6), (1, 4), (2, 9)?

Answer 1

To find the equation of the parabola passing through the points (-1, 6), (1, 4), and (2, 9), we need to solve a system of three equations to find the values of a, b, and c. The equation of the parabola is y = -1.5x^2 + 6.5x + 3.5.

Step-by-step explanation:

The equation of a parabola in standard form is y = ax^2 + bx + c. To find the equation of the parabola passing through the points (-1, 6), (1, 4), and (2, 9), we need to solve three equations to find the values of a, b, and c.

1. Substituting the coordinates of each point into the equation, we get a set of three equations.
2. Using a system of three equations with three variables, we can solve for a, b, and c.
3. Once we have the values of a, b, and c, we can plug them into the standard form equation to write the equation of the parabola.

After solving, the equation of the parabola passing through the given points is y = -1.5x^2 + 6.5x + 3.5.