the graph of y = x² is the solid black graph below. which function represents the dotted graph?
the graph of y = x² is the solid black graph below. which function represents the dotted graph?
Answer
Explanation:
Step1: Identify transformation
The dotted - graph is a vertical translation of the graph (y = x^{2}) downwards. The general form of a vertical translation of a function (y = f(x)) is (y=f(x)+k), where (k\lt0) for a downward translation.
Step2: Determine the value of (k)
By observing the graph, the vertex of (y = x^{2}) is ((0,0)) and the vertex of the dotted - graph is ((0, - 2)). So the function of the dotted - graph is (y=x^{2}-2).
Answer:
(y = x^{2}-2)