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y=x^2-4x-32

 Aug 18, 2017
 #1
avatar+2340 
+1

What do you need help with here? Graphing? Factoring? Finding the roots? You haven't made it clear.

 Aug 18, 2017
 #2
avatar+171 
+1

 factoring and tell whether the parabola opens  up or down. Also Identify the minimum and how does the axis of symmetry  relate to the x-intercepts? 

BOSEOK  Aug 18, 2017
 #3
avatar+98197 
+3

Factoring and tell whether the parabola opens  up or down. Also Identify the minimum and how does the axis of symmetry  relate to the x-intercepts? 

 

y=x^2-4x-32

 

Note that the form  is y = x^2 + bx + c

 

factoring and tell whether the parabola opens  up or down. Also Identify the minimum and how does the axis of symmetry  relate to the x-intercepts? 

 

Since x^2 is positive and there  is no negative in front of the y, term, this parabola opens upward

 

Factoring  we have....  y =  ( x - 8) ( x + 4)

 

Setting   y  = 0, we can find the  x intercepts  thusly :   0 = (x - 8) ( x + 4).....setting each of these factors to 0 and solving for x  produces the x intercepts of x = 8   and x  = -4

 

The minimum  can be found thusly :

 

The x coordinate of the vertex  is given  by      -b / [ 2a ]   ....b = -4   and a = 1   .....so   ....   -b / [2a ] =  -[ -4] / [ 2(1)]   =

2

 

Now....we can find the y coordinate of the vertex  by plugging this value into the function...so we have ...

y = (2)^2 - 4(2) - 32  =  4 - 8 - 32  =  4 - 40  = -36    .....and this is the minimum y value of the parabola

 

The axis of symmetry will be found between the  intercepts  and is given  by adding the intercepts and dividing by  2....so we have ... [ 8 + -4 ] / 2 =  4 / 2  = 2.......so the axis of symmetry   is x = 2....this is no coincidence.....the axis of symmetry will occur at the vertex which is ( 2 , - 36)

 

 

 

cool cool cool

 Aug 18, 2017
 #4
avatar+71 
+2

Trouble factoring a quadratic?  Easy when you realise that   ----

 

 The factors of the constant term add up to the value of the co-efficient of  x

 

Here you have x^2 - 4x - 32.     We want the factors of   -32    that add up to      -4   because that is the

co-efficient  of x  here.

factors of -32  are plus or minus16 and plus or minus 2

and plus or minus 8 and plus or minus 4.         Since there is no way we can get - 4 from the sums of

plus or minus 16 and 2    we look at plus or minus 8 and 4.     The only possible sum is -8  + 4.

So the factors are  (x-8)(x+4)     Try a few more and you'll soon get the technique.

 Aug 18, 2017

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