Question

How many times with the graphs of f(x) equals X squared minus 6X +2 and g(x) equals 5X +2 intersect?

Answer 1

2 times

Explanation:

Given:

• f(x) = x² - 6x + 2 (blue line)
• g(x) = 5x + 2 ( green line)

To find:

• No. of interesetion

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.