With algebra and show work : ) an explanation would be nice too because this topic confuses me : / the function f(t) = t^2 + 4t − 14 represents a parabola. part a: rewrite the function in vertex form by completing the square. show your work. part b: determine the vertex and indicate whether it is a maximum or a minimum on the graph. how do you know? part c: determine the axis of symmetry for f(t).

A.

B.

It's a minimum, becuase .

C.

The axis of symmetry is . So, in this case, it's .

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