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What would be the considering function f(x) = x^2 + 4x +1? How would I find the...

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windieokie | Student, College Freshman | eNotes Newbie

Posted February 2, 2009 at 5:21 AM via web

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What would be the considering function f(x) = x^2 + 4x +1? How would I find the x-coordinate of vertex of this parabola?

Once I get this answer I can complete the table to graph my function.

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giorgiana1976 | College Teacher | Valedictorian

Posted February 2, 2009 at 5:32 AM (Answer #1)

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In order to find out the x coordinate of f(x)'s vertex, you have to know the coordinates of vertex.

If the function is f(x)=ax^2+bx+c, the coordinates of vertex are:

x coordinate= -b/2a

y coordinate = -delta/4a

delta=b^2- 4ac

So, a=1, b=4, c=1 from

f(x) = x^2+4x+1

x coordinate=-4/2*1=-2

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neela | High School Teacher | Valedictorian

Posted June 10, 2009 at 8:37 PM (Answer #2)

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The standard form of the parabola is:

Y^2= 4aX. Its vertex  is at cordinates:(0,0)and focus is at(a,0), Similarly,

x^2= 4ay is a parabola, with vertex at (0,0) and focus at (0,a)

Given form is  f(x) =x^2+4x+1 .

f(x) =(x+2)^2  - 2^2  +1

f(x)=(x+2)^ -3

f(x)+3=(x+2)^2  or

(x+2)^2= y-3

(x+2)^2= 4(1/4)(y-3) which is of the form,

X^2= 4aY.

Therfore, (X,Y) = (0,0) gives :

x+2=0 and  y-3=0

x=-2 and y=3.

Therefore, the vertex coordinates are (x,y)= (-2, 3).

The x coordinate is -2

 

 

 

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revolution | College Teacher | Valedictorian

Posted September 9, 2010 at 12:50 PM (Answer #3)

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Consider this equation:

ax^2+bx=0

x(ax+b)=0

x=0 or ax+b=0

x=0 or ax=-b

x=0 or x=-b/a

So, the two x-intercepts therefore would be 0 and -b/a

Getting the average of the two x-intercepts, which would be the vertext of the curve, then the vertex is:

average= (0-b/a)/2= (-b/a)/2= -b/2a (vertex point)

Now, let's look at the quadratic equation, f(x) (or y)= x^2+4x+1

-b/2a= -4/2(1)= -4/2= -2 (x-coordinate)

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