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I have a function where the graph is y=0 on x=-0,5 and x=6,5

The graph cuts the y-axis at 0;1

What I want to do it so write out the quadratic function based on the information I have.

I tried figuring it out doing the following:

 

k(0+0,5)(0-6,5) = 1

k * 0,5 * -6,5 = 1

(K * -3.25)/-3,25 = 1/-3,25

K = 0.3076923076923077

f(x) = 0.31(x+0,5)(x-6.5)

f(x) = 0.31(x^2+x-3,25)

f(x) = 0,31x^2+0,31x-1,0075

 

The graph shown in my book is not accurate to the one I get written out trying to calculate it, so I wonder what I did wrong.

 

Would love some help!

Guest May 6, 2017
 #1
avatar+89709 
+2

 

We can write

 

y = a( x - 0.5) ( x - 6.5)

 

And we know that   (0, 1)  is on the graph.....so

 

1 = a ( 0 - 0.5) (0 - 6.5)

 

1  = a ( -0.5) ( - 6.5)

 

1  =  a ( 3.25)

 

a  =  1 / 3.25   =  4/13

 

So  our function  becomes

 

y = (4/13) (x - 0.5) ( x - 6.5)

 

y = (4/13) ( x^2 - 7x + 3.25) 

 

y = (4/13)x^2 -  (28/13)x  + 1 

 

Here's the graph :  https://www.desmos.com/calculator/tgzjgr00sz

 

 

cool cool cool

CPhill  May 6, 2017
 #2
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0

You worked it out much better than me, thank you!

 

However, the graph that shows in my textbook is actually a negative one with a max point rather than a mininal point as teh graph you showed me is :(

 

Also, how does 2x * 0,5 become 7x?

 

Glad for answers!

Guest May 6, 2017
 #3
avatar+89709 
+2

Sorry....I didn't   see the  (-)  in front of the  "0.5 "

 

Let me rework this.....it will be a similar process....

 

We can write

 

y = a( x + 0.5) ( x - 6.5)

 

And we know that   (0, 1)  is on the graph.....so

 

1 = a ( 0 +0.5) (0 - 6.5)

 

1  = a ( 0.5) ( - 6.5)

 

1  =  a (- 3.25)

 

a  =  -1 / 3.25   = - 4/13

 

So  our function  becomes

 

y = (-4/13) (x + 0.5) ( x - 6.5)

 

y = (-4/13) (x^2 - 6x - 3.25)

 

y =  (-4/13)x^2 + (24/13)x + 1

 

Here's the graph :  https://www.desmos.com/calculator/r3el9qubfe

 

Sorry about that   !!!!

 

 

cool cool cool

CPhill  May 6, 2017
 #4
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0

Aight cool, thanks!

 

Just one last question, where does the 6x come from?

Isn't 2x*0,5 just 1? :o 

Guest May 6, 2017
 #5
avatar+89709 
+2

Note  what happens when we expand   (x + 0.5) ( x - 6.5)

 

Distribute the terms in the first set of parentheses over the terms in the second set

 

x ( x - 6.5)  +  0.5 ( x - 6.5)   =

 

x^2  - 6.5x  + 0.5x - 3.25        combine like terms

 

x^2  - 6x  -  3.25

 

Now just apply the (-4/13)  over these to get the final function

 

 

 

 

cool cool cool 

CPhill  May 6, 2017
 #6
avatar
+1

Ah right!

Thank you once again!

Guest May 6, 2017

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