# Bringing it All Together

Consider transforming the function, $$f(x) = x^2$$ three units right and five units up. Explain to your partner what the new algebraic form of the function will look like. Justify your reasoning.

Graph your new function.

As we wrap up this section of the module how would you generalize the parent function $$f(x)=x^2$$ so that the transformations would easily described without having to graph the function?

One possible generalized equation is the vertex form of a quadratic function, which is $$f(x)=a(x-h)^2+k$$ where $$k$$ is the vertical shift and $$h$$ is the horizontal shift.  What do you have to remember about the horizontal shift?