Question

Quadratic Quilts

Optima has a quilt shop where she sells many colorful
quilt blocks for people who want to make their own
quilts. She has quilt designs that are made so that they can be sized to fit any bed. She
bases her designs on quilt squares that can vary in size, so she calls the length of the
side for the basic square x, and the area of the basic square is the function A(x) = x^2. In this
way, she can customize the designs by making bigger squares or smaller squares.

Solve for X. Simplify your answer as much as possible.

a. x = 0
b. x = 1
c. x = x^2
d. x = √A(x)

Answer 1

The correct answer to the student's question is 'd. x = √A(x)', since this represents the side length x of the quilt square given the area A(x) as a function of x squared.

Step-by-step explanation:

The student is asking about solving for x in the context of a quadratic function, where the area of a quilt square, A(x), is given by the function A(x) = x^2. To find the side length (x) of the square, we need to solve the equation for x. Since the area function is A(x), and we are given that A(x) = x^2, we can rewrite this equation to find the side length x as x = √A(x). This involves taking the square root of the area to find the side length. Thus, the answer that simplifies the relationship between x and A(x) is d. x = √A(x).