Find g(x), where g(x) is the translation 10 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 \( g(x) \) as a translation of the function \( f(x) = x^2 \) down by 10 units, we need to subtract 10 from the original function.

Starting with \( f(x) \): \[ f(x) = x^2 \]

Translating this down by 10 units gives us: \[ g(x) = f(x) - 10 = x^2 - 10 \]

Now, we can rewrite \( g(x) \) in the form \( a(x - h)^2 + k \). We can identify \( a \), \( h \), and \( k \) directly from \( g(x) = x^2 - 10 \):

• Here, \( a = 1 \),
• \( h = 0 \) (since there’s no horizontal shift),
• \( k = -10 \).

Putting this together, we have: \[ g(x) = 1(x - 0)^2 - 10 \]

Thus, the final answer is: \[ g(x) = 1(x - 0)^2 - 10 \]

To summarize: \[ g(x) = (x - 0)^2 - 10 \]

In integer form, \( a = 1 \), \( h = 0 \), and \( k = -10 \).

Final answer: \[ g(x) = (x - 0)^2 - 10 \]