The graph of the function f(x) = x² -14x + 40 intersects the x-axis at the points x = 10 and x = 4.
Let's find the points where the graph of the function f(x) = x² -14x + 40 intersects the x-axis. This means we need to solve the equation f(x) = 0.
We can solve the equation using the quadratic formula, which is a general formula for solving quadratic equations. The formula is:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -14, and c = 40.
Plugging these values into the formula, we get:
x = (-(-14) ± √((-14)² - 4 * 1 * 40)) / (2 * 1)
x = (14 ± √(196 - 160)) / 2
x = (14 ± √36) / 2
x = (14 ± 6) / 2
Separating the equations, we get:
x = 10
x = 4
Therefore, the graph of the function f(x) = x² -14x + 40 intersects the x-axis at the points x = 10 and x = 4.