Answer:
2 times
Explanation:
Given:
- f(x) = x² - 6x + 2 (blue line)
- g(x) = 5x + 2 ( green line)
To find:
Solution:
The graphs of f(x) and g(x) intersect when f(x) = g(x). Therefore, we need to solve the equation f(x) = g(x).
Substituting the expressions for f(x) and g(x), we get:
x² - 6x + 2 = 5x + 2
Subtracting 5x + 2 from both sides, we get:
x² - 6x + 2 -5x - 2 = 5x + 2 -5x - 2
x²- 11x = 0
Factoring the left-hand side, we get:
x(x - 11) = 0
Either
x = 0
or
x - 11 = 0
x = 11
So, the graphs of f(x) and g(x) intersect at x = 0 and x = 11.
Therefore, the graphs of f(x) and g(x) intersect two times.