Question

What is the equation of the parabola passing through the points (1,7), (2,2), and (4,-32)?

A. Y = -4x^2
B. Y = x^2 - 4
C. Y = 4x^2
D. Y = 4 - x^2

Answer 1

To find the equation of a parabola through three points, plug the points into the general quadratic equation form y = ax^2 + bx + c, and solve the resulting system of equations for a, b, and c.

Step-by-step explanation:

The equation of the parabola passing through the points (1,7), (2,2), and (4,-32) can be determined using a system of equations where the general form of a quadratic is y = ax2 + bx + c. By substituting the x and y values of each point into the equation, we get a system of equations that can be solved for a, b, and c.

For point (1,7): 7 = a(1)2 + b(1) + c
For point (2,2): 2 = a(2)2 + b(2) + c
For point (4,-32): -32 = a(4)2 + b(4) + c

Solving this system will give us the exact values of the coefficients a, b, and c, which can then be used to write the final equation of the parabola.