Question

F(x) = 2x² + 4x + 5; shifts 2 units up and 3 units right.+2

Answer 1

Given any quadratic function as shown below

`f(x)=ax^2+bx+c`

To shift left or right, then the quadratic function becomes

`\begin{gathered} f(x)=a(x\pm h)^2+b(x\pm h)+c \\ \text{Where h is the shift unit to left or right} \end{gathered}`

To shift the up or down, the quadratic function becomes

`\begin{gathered} f(x)=a(x\pm h)^2+b(x\pm h)+c\pm k \\ \text{Where k is the shift up or down} \end{gathered}`

Given the quadratic function below

`f(x)=2x^2+4x+5`

To shift 2 units up and 3 units right would make the fucntion becomes

`\begin{gathered} f(x)=2(x-3)^2+4(x-3)+5+2 \\ f(x)=2(x-3)^2+4(x-3)+7 \\ f(x)=2(x^2-6x+9)+4x-12+7 \\ f(x)=2x^2-12x+18+4x-12+7 \end{gathered}`
`f(x)=2x^2-8x+13`

Hence, the final answer is 2x²-8x+13