Question

n two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x-2)2 -3. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answer 1

f(x) intersects x-axis at one point (0 , 0)

g(x) intersects x-axis at two points (2-√3 , 0) , (2+√3 , 0)

g(x) is the image of f(x) when f(x) moved right 2 units and

moved down 3 units

Explanation:

∵ f(x) = x²

∵ x-intercept means f(x) = 0

∴ x² = 0 ⇒ x = 0

∴ The parabola intersect x-axis at one point (0 , 0)

∵ g(x) = (x - 2)² - 3

∵ x-intercept means g(x) = 0

∴ (x - 2)² - 3 = 0

∴ (x -2)² = 3 ⇒ take square root for both sides

∴ (x - 2) = -√3 ⇒ x = 2 - √3

∴ (x - 2) = √3 ⇒ x = 2 + √3

∴ The parabola intersect x-axis at two points (2-√3 , 0) , (2+√3 , 0)

∵ f(x) = x² , g(x) = (x - 2)² - 3

∴ g(x) is the image of f(x) when :

f(x) moved right 2 units and moved down 3 units