Question 921157: 4x^2+24x-13 converted into vertex form
Found 2 solutions by srinivas.g, Edwin McCravy:
Answer by srinivas.g(540)   (Show Source):
You can put this solution on YOUR website! The vertex form of a parabola is given by y = a(x - h)^2 + k, a ≠ 0.
standard form is y= ax^2+bx+c
Comparing with the standard form of parabola, f(x) = ax^2 + bx + c, we get
a = 4.
given equation y= 4x^2+24x-13
y = (2x)^2 -2*2x*6-13
to make it perfect square add 6^2 and subtract 6^2
y = (2x)^2 -2*2x*6-13+6^2-6^2
y=(2x)^2 -2*2x*6+6^2 -13-6^2
y= (2x-6)^2-13-36
y =(2x-6)^2 -49
take 2 out side in square term
y = 2^2 *( x-3)^2 -49
y= 4 (x-3)^2-49
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
Maybe the other tutor didn't break it down enough for you
to understand. Some people require a little more breakdown
and explanation than others. Here is the complete breakdown
all the way to the graph. Study it carefully and use it as
a model for your other problems and you'll know how to do them
all.
Factor 4 out of the first two terms. (Don't factor out 4x, just 4)
To the side:
Multiply the coefficient of x, which is 6, by  . 
Square 3. 
Add +9-9 to the 6x inside the parentheses. (It doesn't affect the value
because adding +9-9 is the same as adding 0.
To the side:
Factor the first three terms inside the parentheses: x²+6x+9 = (x+3)(x+3)
Write (x+3)(x+3) as (x+3)².
Replace x²+6x+9 by (x+3)²
Remve the BIG parentheses (not the small ones) by distributing the 4
into the BIG parentheses leaving the small parentheses intact:
Combine the -36-13 as -49
That's it. Compare it to
And see that -h = +3 which means h = -3
+k = -49 which means or k = -49
Which means the vertex point is (h,k) = (-3,-49)
and that the graph passes through the three points
1. The vertex = (h,k) = (-3,-49)
2. The point just to the right of the vertex: (h+1,k+a) = (-3+1,-49+4) = (-2,-45)
3. The point just to the left of the vertex: (h-1,k+a) = (-3-1,-49+4) = (-4,-45)
Plot those three points and sketch the graph:
Edwin
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