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# Write out the quadratic function based on zero values in a graph

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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
+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

CPhill  May 6, 2017
#2
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?

Guest May 6, 2017
#3
+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

CPhill  May 6, 2017
#4
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
+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

CPhill  May 6, 2017
#6
+1

Ah right!

Thank you once again!

Guest May 6, 2017