+0

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

0
129
6

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
Sort:

#1
+76972
+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
+76972
+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
+76972
+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

### 4 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details