Question

For the equation
`y = (x - 4)^2`, find the parent function, type of translation, domain, and range.

a) Parent function:
`y = x^2`
b) Type of Translation: Horizontal shift 4 units to the right
c) Domain: All real numbers
d) Range: [0, [infinity])

Answer 1

The equation y = (x - 4)^2 has a parent function y = x^2, is translated 4 units to the right, has a domain of all real numbers, and a range of [0, infinity).

Step-by-step explanation:

To answer the question regarding the equation y = (x - 4)^2:

1. The parent function is y = x^2. This is the simplest form of a quadratic function and serves as the base for the given equation.
2. The type of translation is a horizontal shift 4 units to the right. This is identified by the subtraction of 4 inside the parentheses, indicating the graph of the parent function is moved to the right along the x-axis.
3. The domain of the function is all real numbers. Since x can take any real value, there is no restriction on the input to the function.
4. The range of the function is [0, ∞). Since the vertex of the parabola is at the point (4,0) and it opens upwards, the y-values can only be greater than or equal to zero.