Question

Function \[g\] can be thought of as a translated (shifted) version of \[f(x)=x^2\]. a parabola labeled f has a vertex at the point 0, 0. a parabola labeled g has a vertex at the point negative 2, 1. \[\small{1}\] \[\small{2}\] \[\small{3}\] \[\small{4}\] \[\small{5}\] \[\small{6}\] \[\small{7}\] \[\small{\llap{-}2}\] \[\small{\llap{-}3}\] \[\small{\llap{-}4}\] \[\small{\llap{-}5}\] \[\small{\llap{-}6}\] \[\small{\llap{-}7}\] \[\small{1}\] \[\small{2}\] \[\small{3}\] \[\small{4}\] \[\small{5}\] \[\small{6}\] \[\small{7}\] \[\small{\llap{-}2}\] \[\small{\llap{-}3}\] \[\small{\llap{-}4}\] \[\small{\llap{-}5}\] \[\small{\llap{-}6}\] \[\small{\llap{-}7}\] \[y\] \[x\] \[\blued{f}\] \[\maroond{g}\] write the equation for \[g(x)\]. \[g(x)=\]

Answer 1

\[g(x)=(x - 2)^2 + 6\]

Step-by-step explanation:

Answer 2

The function g(x) is a translated version of f(x) = x^2 with a vertex at (-2, 1), which gives us the equation g(x) = (x + 2)^2 + 1.

Step-by-step explanation:

When given a function f(x) = x^2, which is a basic quadratic function, and an indication that function g is a translated version of f(x), we can deduce the equation of g(x) by considering the given vertex of g, which is (-2, 1). To shift the parabola f(x) = x^2 to the left by 2 units and up by 1 unit, we apply horizontal and vertical transformations to the equation of f(x). This results in g(x) = (x + 2)^2 + 1. This equation represents a parabola that has been shifted to the left by 2 units (indicated by x + 2) and up by 1 unit (indicated by + 1).