If the domain of the function f(x) = –2x^2 – 3 is {-1,2,5), then the range is A. {-53-11, 5)
B. {1, 13,97)
C. {-13,-7, -1)
D. {-13,-11, 1)

i’m here for points.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4