Question 177856: Write each function in vertex form. Sketch the graph of the function and
label its vertex.
33. y = x2 + 4x - 7
34. y = -x2 + 4x - 1
35. y = 3x2 + 18x
36.y = 1/2x2 - 5x + 12
Found 2 solutions by stanbon, jojo14344:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write each function in vertex form. Sketch the graph of the function and
label its vertex.
33. y = x^2 + 4x - 7
x^2 + 4x + ? = y+7+?
x^2 + 4x + 4 = y+7+4
(x+2)^2 = y + 11
-----------------
Vertex: (-2,-11)
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34. y = -x^2 + 4x - 1
35. y = 3x^2 + 18x
-------------------------
36.y = 1/2x^2 - 5x + 12
(1/2)x^2 - 5x + ? = y-12 + ?
(1/2)[x^2 - 10x + ? = y-12 + ?
(1/2)[x^2 - 10x + 25] = y - 12 + (1/2)*25
(1/2)[x-5]^2 = y + (1/2)
----
Vertex: (5,-1/2))
============================
Cheers,
Stan H.
Answer by jojo14344(1513) (Show Source):
You can put this solution on YOUR website!
We know the standard eqn of a parabola: 
Being the vertex form----> , where (h,k) is the vertex:
I'll do the first one, and you can continue the rest;
33.  --->follows std eqn, where
Complete the square, adding a constant by taking half of the "b" constant then squared. In this case the "b" constant is  , half of it  then squared,  :
 , Also subtract what you added so the process won't change.
 ---->it follows the vertex form, being 
To get the x-intercept, we solve the eqn by Quadratic:
where---->
For the Y-Intercept, let 
As we see the graph:
Thank you,
Jojo
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