question is down there it was to big for here....?

Question

Find the vertex of the parabola y = -3(x - 2)^2 + 4. Give your answer
by filling in the blanks in the following sentence, where the first
blank is the coordinates of the vertex, and the second blank is either
the word "highest" or the word "lowest".

The vertex is ______ , and this point is the _________ point on the
parabola.

Answer 1

(2,4) highest
In general, when you have the parabola written in the form
y = a(x-k)^2 + h,
the vertex is at (k,h)
You can think of tihs as horizontal and vertical translations of the basic parabola y=x^2, which opens upward and has its vertex, its lowest point, at 0. Notice that horizontal translations work opposite to the sign, that's because the effect of the translation is to make the fuction do at 2 what it would otherwise do at 0.
You can also think of the a as a stretch, shrink, or flip of the basic parabola. Since a = -3 and -3 < 0, this amounts to a flip or inversion thru the x axis, turning the parabola upside down so that its vertex occurs at the highest point rather than the lowest point.
To better understand things like this, there are places online where you can see good explanations of parabolas and translations. Just put function translations tutorial and parabola tutorial into your your search window.
For example ...
http://www.purplemath.com/modules/fcntrans.htm
http://ellerbruch.nmu.edu/classes/.../para.tutorial/para.mainmenu.html
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut34_quadfun.htm
When you understand math, you can do it.

Answer 2

Of course she-nerd is correct, but do you need any explanation?

OK, forget the rest of mine, I see she's given you a thorough account.

The simplest parabola is y = x^2, whose vertex is its lowest point -- i.e. it is concave upwards -- and is the origin, (0,0)

If we multiply by a constant "a", the vertex stays the same but the parabola gets "fatter" or "thinner", and if a is negative then the parabola is concave downwards, i.e. it's turned "upside down".

If we replace x by x-h and y by y-k, giving
y-k = a(x-h)^2
the vertex is moved to (h,k)

The example you've given here can be written as
y-4 = -3(x-2)^2, so that

(h,k) = (2,4) and a = -3. Since a is negative the parabola is concave downwards, and so the vertex is at the highest point.