Answer:
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
Step-by-step 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
