Question

Determine the quadratic function f whose vertex is (3,-6) and the other given point is (-1,2).

Answer 1

To determine the quadratic function f whose vertex is (3,-6) and the other given point is (-1,2), we can use the vertex form of a quadratic function and substitute the given values to find the value of 'a'. The quadratic function f is f(x) = (1/2)(x-3)^2 - 6.

Step-by-step explanation:

To determine the quadratic function f whose vertex is (3,-6) and the other given point is (-1,2), we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k, where (h,k) is the vertex. Substituting the given values, we have f(x) = a(x-3)^2 - 6. To find the value of 'a', we substitute the coordinates of the other given point (-1,2) into the equation and solve for 'a'.

1. Substitute x = -1 and f(x) = 2 into f(x) = a(x-3)^2 - 6.
2. 2 = a(-1-3)^2 - 6
3. 2 = a(-4)^2 - 6
4. 2 = 16a - 6
5. 16a = 2 + 6
6. 16a = 8
7. a = 8/16
8. a = 1/2

Therefore, the quadratic function f is

f(x) = (1/2)(x-3)^2 - 6

.