Question

Name the Parent Function and Describe how you know what the parent function is for the equation y = 3(x - 1)² - 2.

a) The parent function is a linear function.
b) The parent function is a quadratic function.
c) The parent function is a cubic function.
d) The parent function is a rational function.

Answer 1

The parent function for the equation y = 3(x - 1)^2 - 2 is a quadratic function, evident by the squared term and the standard vertex form of a quadratic.

Step-by-step explanation:

The parent function for the equation y = 3(x - 1)² - 2 is a quadratic function. We can determine this because the equation is in the form of y = a(x - h)² + k, where a, h, and k are constants, and the variable x is squared. This form is known as the vertex form of a quadratic function, indicating that the underlying parent function is y = x², which is a second-order polynomial or a quadratic function. Therefore, the correct answer is b) The parent function is a quadratic function.