Question

The graphs below have the same shape. What is the equation of the graph ofx)?A 9=×-2B. g(x) =(x-2)²C. g(x) = (x+ 2)²D. g(x) = 22 + 2

Answer 1

Based on the graph, the f(x) graph is the graph of the parent function of a quadratic function which is f(x) = x².

Now, as we can see on the graph, the g(x) graph is basically the same graph but is translated two units to the left of the f(x) graph.

If a graph is translated two units to the left, we are going to add "2" to the "x" variable of the original function.

Therefore, the equation of g(x) is g(x) = (x + 2)². (Option C)

`\begin{gathered} f(x)=x^2 \\ g(x)=(x+2)^2 \end{gathered}`