Given point a(6, 12), point b(15, –4), and point c(20, 12), find the coordinates of the point that partitions the directed line segment into the given ratio.

directed line segment

ratio 1 : 1

directed line segment

ratio 5 : 2

directed line segment

ratio 2 : 3

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step-by-step explanation:

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(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.