Question

The length of a rectangle is 9 inches more than twice the width, w, of the rectangle. The quadratic function, A(w) represents the area A, in square inches, of the rectangle for a given value of w.

Answer 1

We can write an equation for the length, L, of the rectangle in terms of its width, w, as:

L = 2w + 9

The area, A, of the rectangle is given by:

A = Lw

Substituting the expression for L into the equation for A, we get:

A = (2w + 9)w

Expanding the right side of the equation, we get:

A = 2w^2 + 9w

Therefore, the quadratic function that represents the area of the rectangle for a given value of w is:

A(w) = 2w^2 + 9w

This function is in standard form, where the coefficient of the squared term is positive. We can also see that the graph of this function is a parabola that opens upwards.