Question

Find an equation in standard form of the parabola passing through the points below. (1, -2), (3,14), (5.38) The equation of the parabola is y=[.​

A) y = 2x^2 + 3x - 4
B) y = -2x^2 + 3x + 4
C) y = 2x^2 - 3x + 4
D) y = -2x^2 - 3x - 4

Answer 1

To find the equation of a parabola passing through given points, substitute the coordinates into the standard form and solve for the constants a, b, and c.

Step-by-step explanation:

The equation of a parabola in standard form is y = ax² + bx + c. To find the equation that passes through the given points, we substitute the coordinates (1, -2), (3, 14), and (5, 38) into the equation and solve for a, b, and c.

1. For the point (1, -2): -2 = a(1²) + b(1) + c
2. For the point (3, 14): 14 = a(3²) + b(3) + c
3. For the point (5, 38): 38 = a(5²) + b(5) + c

Solving this system of equations will give us the values of a, b, and c, which we can then use to write the equation of the parabola in standard form.