A train traveled 400 miles in 9 hours. The speed of the train for the first part of the journey was 40 miles per hour what the speed for the second part of the journey was 59 miles per hour. Find the distance traveled when the train was traveling at 59 miles per hour.

(a) x intercepts: -6 and 2

you can obtain these by solving the equation 0=x^2 +4x-12 using your favorite quadratic formula. but it is easy to verify -6 and 2 indeed satisfy this equation.

(b) y intercept: -12

this is obtained by setting x=0: 0^2+4*0-12 = -12

(c) the minimum value is: -16 (this is the vertex)

you can get the vertex by rewriting the equation into the form:

there is no global or local maximum as the function goes to infinity, so only in the limit sense: +infinity.