How is the graph of $g (x) = x^{2} - 2$ $g(x)=x^2-2$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?

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Answer 1 · 2017-07-26T03:15:20

Both are functions, only difference (equation-wise) is the $c$ $c$ -value, which causes $g (x)$ $g(x)$ to translate $2$ $2$ units down.

The only difference between the two (equation-wise) is the $c$ $c$ -value .

The $c$ $c$ -value controls the vertical translation of a function.

With $- 2$ $-2$ as the value, $g (x)$ $g(x)$ goes down $2$ $2$ units.

We can prove this with a graph.

graph{(y-x^2)(y-x^2+2)=0 [-16.16, 12.31, -7.46, 6.77]}

The graph with the lower vertex is $g (x)$ $g(x)$ .

Hope this helps :)

How is the graph of g(x)=x^2-2g(x)=x2−2g(x)=x^2-2 related to the graph of f(x)=x^2f(x)=x2f(x)=x^2?