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**+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

#3**+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 !!!!

CPhill
May 6, 2017

#5**+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