The quadratic function f(x) = x? is transformed to create the graph of g(x) = f(x - c) + d, where d is a positive
number. Select three points that represent a possible vertex of the graph of g.
Select THREE correct answers.
To find the vertex of the function g(x) = f(x - c) + d, we need to find the values of x that will result in the minimum or maximum value for g(x).
The original function f(x) = x has a vertex at (0, 0).
By subtracting c from x, we will shift the graph horizontally to the right by c units. So, the x-coordinate of the vertex of g(x) will be c.
By adding d to f(x-c), we will shift the graph vertically upwards by d units. So, the y-coordinate of the vertex of g(x) will be d.
Therefore, the vertex of g(x) will be (c, d).
Possible options for three points that represent a possible vertex of g(x) are:
- (c, d)
- (c+1, d)
- (c-1, d)
where c and d are positive numbers.