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.

The basic quadratic function is f(x) = x²

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

Step-by-step 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

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step-by-step explanation:

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