Question

Quadratic Functions write the equation for each of the following. start with the graph of f(x) =x²1- Shift 3 units left and 6 units down.

Answer 1

`(\text{ x }+3)^2-\text{ 6}`

Step-by-step explanation:
`\begin{gathered} f(x)=x^2 \\ \text{translation to the up:} \\ f(x)\text{ + d} \\ \text{translation to the down:} \\ f(x)\text{ }-\text{ d} \end{gathered}`
`\begin{gathered} \text{translation right:} \\ f(x-d)\text{ } \\ \text{translation left:} \\ f(x\text{ + d)} \end{gathered}`
`\begin{gathered} \\ \text{translation of }3units\text{ }left=(\text{ x }+3)^2 \\ \text{followed by translation 6 units down = }(\text{ x }+3)^2-\text{ 6} \end{gathered}`
`\begin{gathered} \text{Equation becomes:} \\ (x+3)^2\text{ - 6} \end{gathered}`