Answer:
Given function:
a)
Th x-intercept found when g(x) = 0
Solve the equation to find the values of x:
- x² - 6x + 2 = 0
- x² - 6x + 9 = 7
- (x - 3)² = 7
- x - 3 = ±√7
- x = 3 ± √7
The x-intercepts are (3 + √7, 0) and (3 - √7, 0)
b)
Solve as above:
- x² - 6x + 10 = 0
- x² - 6x + 9 + 1 = 0
- (x - 3)² = -1
The left side is a square of a number which is always positive, the right side is negative.
It means there is no solution, so no-x-intercepts.
The graph of the function lies above the x-axis.