Graph

f

(

x

)

=

x

2

-

10

x

+

24

f (x) = x2-10x+24.

F (x) = x^2 - 10x + 24 = (x - 4) (x - 6) i. e. f (x) crosses the x-axis at x = 4 and x = 6.

f (x) written in vertex form is (x - 5) ^2 - 1 meaning that the vertex is (5, - 1)

Therefore, the graph of f (x) is a parabola facing up with vertex at (5, - 1) and x-intercepts at x = 4 and x = 6.