To determine the x-intercept of the function that translates the original function \( f(x) = x^2 \) down by 4 units, we first need to write the equation for the translated function.
A downward translation of 4 units can be represented as:
\[ g(x) = f(x) - 4 = x^2 - 4 \]
Next, we find the x-intercepts of the function \( g(x) \). The x-intercepts occur where \( g(x) = 0 \):
\[ x^2 - 4 = 0 \]
Now, we solve for \( x \):
\[ x^2 = 4 \]
Taking the square root of both sides yields:
\[ x = \pm 2 \]
Thus, the x-intercepts of the function \( g(x) = x^2 - 4 \) are:
\[ x = 2 \quad \text{and} \quad x = -2 \]
In conclusion, the x-intercepts of the function that translates \( f(x) = x^2 \) down 4 units are \( x = 2 \) and \( x = -2 \).
1 answer