MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

Answer:The basic quadratic function is f(x) = x²The equation of the graph is y = (x - 3)² - 1Step-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