Question

The following graph is the result of applying a sequence of transformations to the graph of one of the six basic functions. Identify the basic function and write an equation for the given graph.

Answer 1

The basic quadratic function is f(x) = x²

The equation of the graph is y = (x - 3)² - 1

Explanation:

* Lets explain how to solve the problem

- The graph is a parabola which oped upward

∵ The function is represented by a parabola

∴ The graph is a quadratic function

∴ The basic quadratic function is f(x) = x²

- The vertex of the basic quadratic function is (0 , 0)

∵ From the graph the vertex of the parabola is (3 , -1)

∵ The x coordinate of the basic function change from 0 to 3

∴ The basic function translate 3 units to the right

- If the function f(x) translated horizontally to the right by h units,

then the new function g(x) = f(x - h)

∵ f(x) = x²

∴ The new function g(x) = (x - 3)²

∵ The y-coordinate of the basic function change from 0 to -1

∴ The basic function translate 1 unit down

- If the function f(x) translated vertically down by k units, then the

new function g(x) = f(x) - k

∵ g(x) = (x - 3)²

∴ The new function h(x) = (x - 3)² - 1

∵ h(x) = y

∴ The equation of the graph is y = (x - 3)² - 1

# Note: you can write the equation in general form by solve the

bracket of power 2

∵ (x - 3)² - 1 = (x)(x) - (2)(3)(x) + (3)(3) - 1 = x² - 6x + 9 - 1 = x² - 6x + 8

∴ y = x² - 6x + 8