SOLUTION: Can you please help with this problem from college algebra blitzer.using this function f(x) =x^2 +4x +1, find h, the x-coordinate of the vertex of this parabola,using a graph. s

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please help with this problem from college algebra blitzer.using this function f(x) =x^2 +4x +1, find h, the x-coordinate of the vertex of this parabola,using a graph. s      Log On


   

Question 124293: Can you please help with this problem from college algebra blitzer.using this function f(x) =x^2 +4x +1, find h, the x-coordinate of the vertex of this parabola,using a graph.
substitute the two intergers immediately to the left and right of h into the function to find the corresponding y. fill in following table. make sure the x- values are in increasing order in your table.


Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find h, use this formula:

h=-b%2F%282a%29

From the equation y=x%5E2%2B4x%2B1 we can see that a=1 and b=4

h=%28-4%29%2F%282%2A1%29 Plug in b=4 and a=1


h=%28-4%29%2F2 Multiply 2 and 1 to get 2



h=-2 Reduce


So the axis of symmetry is x=-2


So the x-coordinate of the vertex is x=-2. Lets plug this into the equation to find the y-coordinate of the vertex.


Lets evaluate f%28-2%29

f%28x%29=x%5E2%2B4x%2B1 Start with the given polynomial


f%28-2%29=%28-2%29%5E2%2B4%28-2%29%2B1 Plug in x=-2


f%28-2%29=%284%29%2B4%28-2%29%2B1 Raise -2 to the second power to get 4


f%28-2%29=%284%29%2B-8%2B1 Multiply 4 by -2 to get -8


f%28-2%29=-3 Now combine like terms


So the vertex is (-2,-3)



Now lets find 2 other points to the left of the vertex


Lets evaluate f%28-4%29

f%28x%29=x%5E2%2B4x%2B1 Start with the given polynomial


f%28-4%29=%28-4%29%5E2%2B4%28-4%29%2B1 Plug in x=-4


f%28-4%29=%2816%29%2B4%28-4%29%2B1 Raise -4 to the second power to get 16


f%28-4%29=%2816%29%2B-16%2B1 Multiply 4 by -4 to get -16


f%28-4%29=1 Now combine like terms


So our 1st point is (-4,1)



----Now lets find another point----



Lets evaluate f%28-3%29

f%28x%29=x%5E2%2B4x%2B1 Start with the given polynomial


f%28-3%29=%28-3%29%5E2%2B4%28-3%29%2B1 Plug in x=-3


f%28-3%29=%289%29%2B4%28-3%29%2B1 Raise -3 to the second power to get 9


f%28-3%29=%289%29%2B-12%2B1 Multiply 4 by -3 to get -12


f%28-3%29=-2 Now combine like terms


So our 2nd point is (-3,-2)


Now remember, the parabola is symmetrical about the axis of symmetry (which is x=-2)
This means the y-value for x=-3 is equal to the y-value of x=-1. So when x=-1, y=-2.
Also, the y-value for x=-4 is equal to the y-value of x=0. So when x=0, y=1.


Now lets make a table of the values we have calculated 



 xy


 -41
 

 -3-2
 

 -2-3
 

 -1-2
 

 01

Now let's plot these points to graph y=x%5E2%2B4x%2B1

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
using this function f(x) =x^2 +4x +1, find h, the x-coordinate of the vertex of this parabola,using a graph.
----------
The max or min point occurs when x=-b/2a = -4/(2*1) = -2
Therefore h=-2
------------------------
substitute the two integers immediately to the left and right of h into the function to find the corresponding y. fill in following table. make sure the x- values are in increasing order in your table.
If x=-4, f(-4) = (-4)^2+4*4+1 = 13
If x=-3, f(-3) = (-3)^2+4*-3+1 =-2
If x=-2, f(-2) = (-2)^2+4*-2+1 =-3
If x=-1, f(-1) = (-1)^2+4*-1+1 =-2
If x=0 , f(0) = (0)^2+4*0+1 = 1
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B4x%2B1%29
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Cheers,
Stan H.