Question

If the points in the table lie on a parabola, write the equation whose graph is the parabola.

X:
-1, 1, 3, 5
Y:
-6, 14, -6, -66
y= ?

Answer 1

The parabola's equation, derived from the given points (-1, -6), (1, 14), (3, -6), and (5, -66), is y = -5x^2 + 4x - 5.

To find the equation of a parabola given a set of points, we can use the standard form of a quadratic equation: y = ax^2 + bx + c. Since we have four points (-1, -6), (1, 14), (3, -6), and (5, -66), we can substitute these coordinates into the equation to form a system of equations.

Substitute (-1, -6): -6 = a(-1)^2 + b(-1) + c

Substitute (1, 14): 14 = a(1)^2 + b(1) + c

Substitute (3, -6): -6 = a(3)^2 + b(3) + c

Substitute (5, -66): -66 = a(5)^2 + b(5) + c

Now, solve this system of equations to find the values of a, b, and c. Once these values are determined, substitute them back into the standard form equation y = ax^2 + bx + c to obtain the equation of the parabola.

After solving, the equation of the parabola is y = -5x^2 + 4x - 5.