Question

The reaction rate of an autocatalytic reaction is given by the formula
R(x)=kx(a-x)
for 0<=x<=a, where a is the initial concentration of substance A and x is the concentration of X.
a) Domain?
b) graph the function for k=3 and a=8

Answer 1

I am confused about part b?

Answer 2

plug in the value of k=3 and a=8 in the equation:
R(x) = kx(a-x) = 3x(8-x)

This is a quadratic expression and the graph of 3x(8-x) will look like a parabola. You can see that for x = 0 and x = 8, 3x(8-x) becomes zero. Those are the roots of the quadratic equation. So the graph will cross the x axis at x = 0 and x = 8.
Also if you expand 3x(8-x) it is 24x - 3x^2. When the coefficient of x^2 is negative the parabola faces down or an inverted parabola.