62. Group Activity Creating Hidden Behavior
You can create your own graphs with hidden behavior. Working in groups of two or three, try this exploration.
(a) Graph the equation y=(x+2)(x2−4x+4) in the window [−4,4] by [−10,10].
(b) Confirm algebraically that this function has zeros only at x=−2 and x=2.
(c) Graph the equation y=(x+2)(x2−4x+4.01) in the window [−4,4] by [−10,10]
(d) Confirm algebraically that this function has only one zero, at x=−2. (Use the discriminant.)
(e) Graph the equation (x+2)(x2−4x+3.99) in the window [−4,4] by [−10,10].
(f) Confirm algebraically that this function has three zeros. (Use the discriminant.)