Question

please explain/give the new equation from the original equation: f(x) = x2 a shifted 3 units down b shifted 4 units right

Answer 1

`\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)= A( Bx+ C)+ D \\\\ ~~~~y= A( Bx+ C)+ D \\\\ f(x)= A√( Bx+ C)+ D \\\\ f(x)= A(\mathbb{R})^( Bx+ C)+ D \\\\ f(x)= A sin\left( B x+ C \right)+ D \\\\ --------------------`


`\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}`


`\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }( C)/( B)\\ ~~~~~~if\ ( C)/( B)\textit{ is negative, to the right}\\\\ ~~~~~~if\ ( C)/( B)\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }(2\pi )/( B)`

and with that template in mind.

3 units down, D = -3

4 units to the right, C = -4

f(x) = (x - 4)² - 3