Answer: [tex]g(x)\text{ = \lparen x + 1\rparen}^2\text{ + 4}[/tex]Explanation:
Given:
[tex]f(x)\text{ = x}^2[/tex]
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):
[tex]\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}[/tex][tex]\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}[/tex]
