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Question

Find g(x), where g(x) is the translation 5 units up of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
g(x)=

Answer 1

To find the function \( g(x) \) which is the translation of \( f(x) = x^2 \) 5 units up, you need to add 5 to the original function. Therefore, we have:

\[ g(x) = f(x) + 5 = x^2 + 5 \]

Now, to write \( g(x) \) in the form \( a(x-h)^2 + k \):

1. Identify \( a \), \( h \), and \( k \):
   • In this case, \( a = 1 \) (since the coefficient of \( x^2 \) is 1),
   • \( h = 0 \),
   • \( k = 5 \).

Thus, \( g(x) \) can be expressed as:

\[ g(x) = 1(x - 0)^2 + 5 \]

So, in the desired form \( a(x - h)^2 + k \):

\[ g(x) = 1(x - 0)^2 + 5 \]

Therefore, the final answer is:

\[ g(x) = 1(x - 0)^2 + 5 \]