Which of the following would illustrate a quadratic relation between the dependent and independent variables when graphed? a. a graph of mass of water vs. the volume of water in a drinking glass b. a graph of the area a of a circle vs. its radius r (a = πr2) c. a graph of the equation a = 1/ b d. a graph of distance vs. time for a car moving at constant speed

option A. a graph of the area of a circle vs. its radius r (A = πr²).

Explanation:

A quadratic relation between the dependent and independent variables shows the independent variable raised to the power of 2.

This is it is a polynomial with general form ax² + bx + c, whewre a, b, and c, named coeficients,  are constants.

The function is y =  ax² + bx + c, where x is the independent variable and y is the dependent variable.

As stated in the question, the area of a circle is given by A = πr².

In this case, A is the dependent variable and r is the independent variable.

π is assumed as the coefficient of the quadratic term, and the other coefficients are assumed 0, since there are no either terms on r or constants.

The equation a = 1/b  is an inverse relation, not a quadratic relation.

The relation of distance vs. time for a car moving at constant speed is a linear relation of the kind v = u + st.

The mass of water vs. the volume of water in a drinking glass is a direct relation, mass = density × volume

Therefore, the only quadratic relation is shown by  a graph of the area of a circle vs. its radius r.