Question

A parabola y = ax² + k passes through the points (-1,3) and (3, -13). Find the values of a and k.

(A) a = -4, k = -1
(B) a = 4, k = 1
(C) a = 2, k = -5
(D) a = -2, k = 5

Answer 1

To find the values of a and k in the parabola equation y = ax² + k, substitute the given points into the equation and solve for a and k. The values of a and k are -2 and 5, respectively.

Step-by-step explanation:

To find the values of a and k in the parabola equation y = ax² + k, we can substitute the coordinates of the given points into the equation.

For the point (-1, 3), we have: 3 = a*(-1)² + k

For the point (3, -13), we have: -13 = a*(3)² + k

This forms a system of two equations. Solving for a and k, we find that a = -2 and k = 5.