Answer:
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
