Question

The graph of g(x) shown below,has the same shape as the graph of f(x)=x^2 but is shifted left by 1 unit and up by 4 units Write the equation for g(x) please help me!

Answer 1

Answer:
`g(x)\text{ = \lparen x + 1\rparen}^2\text{ + 4}`Step-by-step explanation:

Given:

`f(x)\text{ = x}^2`

To find:

the equation for g(x) after a translation of 1 unit to the left and 4 units up

The graph of f(x) will show the tip of the parabola at the origin (0, 0)

We will apply the translation rule to get g(x):

`\begin{gathered} f(x\text{ + a\rparen is a translation to the left} \\ f(x)\text{ + d is a translation up} \\ where\text{ a and d are the number of movement respectively} \end{gathered}`
`\begin{gathered} translation\text{ of 1 unit to the left:} \\ (x\text{ + 1\rparen}^2 \\ trnaslation\text{ of 4 units up:} \\ (x\text{ + 1\rparen}^2\text{ + 4} \\ \\ g(x)\text{ = \lparen x + 1\rparen}^2\text{ + 4} \end{gathered}`