Question

Linear functions (with the exception of f(x) = x) can have at most one fixed point. Quadratic functions can have at most two. Find the fixed points of the function g(x) = x 2 − 12.
Give a quadratic function whose fixed points are x = −2 and x = 3.

Answer 1

Answer:

a. x = 3.46 or -3.46. b. x²- x - 6 = 0

Step-by-step explanation:

At the fixed point, g(x) = 0. So, x² - 12 = 0 ⇒ x² = 12 ⇒ x = ±√12

x = 3.46 or -3.46.

The quadratic equation whose fixed points are x = -2 and x = 3. The fixed points are the roots of the quadratic function.

Using x² - (sum of roots)x + product of roots = 0.

x² -(-2 + 3)x + (-2)(3) = 0

x² - (1)x - 6 = 0

x²- x - 6 = 0