Find g(x), where g(x) is the translation 7 units down of f(x)=x2.

Question

Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
g(x)=

Answer 1

To find \( g(x) \), which is the translation of \( f(x) = x^2 \) 7 units down, we need to subtract 7 from the function.

Starting with the original function:

\[ f(x) = x^2 \]

To translate this down by 7 units, we modify the function as follows:

\[ g(x) = f(x) - 7 = x^2 - 7 \]

Now, we need to express this in the form \( a(x - h)^2 + k \).

In this case, since \( f(x) \) is already in the vertex form \( a(x - h)^2 + k \):

\[ g(x) = 1(x - 0)^2 - 7 \]

Here, \( a = 1 \), \( h = 0 \), and \( k = -7 \).

Thus, we can write:

\[ g(x) = 1(x - 0)^2 - 7 \]

Final answer:

\[ g(x) = 1(x - 0)^2 - 7 \]

Or simplified:

\[ g(x) = (x - 0)^2 - 7 \]

So, in the requested form:

\[ g(x) = 1(x - 0)^2 - 7 \] or simply:

\[ g(x) = (x - 0)^2 - 7 \]

This gives the values:

• \( a = 1 \)
• \( h = 0 \)
• \( k = -7 \)