Finding a quadratic function based on the graph

• Mar 4th 2010, 02:22 PM
Finding a quadratic function based on the graph
Hello,

I have a problem in a homework assignment that's asking me to take the graph of a quadratic function and write a quadratic function that fits the graph. I thought this would be more straightforward but I'm finding myself stumped.

The zeros of the graph are (0,0) and (10,0) and the vertex is (5,8). How would I use this information to write a quadratic function?

• Mar 4th 2010, 03:56 PM
skeeter
Quote:

Hello,

I have a problem in a homework assignment that's asking me to take the graph of a quadratic function and write a quadratic function that fits the graph. I thought this would be more straightforward but I'm finding myself stumped.

The zeros of the graph are (0,0) and (10,0) and the vertex is (5,8). How would I use this information to write a quadratic function?

since x = 0 and x = 10 are roots of the quadratic ...

y = kx(x-10)

now use the fact that y = 8 when x = 5 to solve for the constant k.
• Mar 5th 2010, 06:11 PM
Hi, thanks for the post.

solving for "k":

8 = k(5)(5-10)
8 = k (5) (-5)
8 = k (-25)
8 = -25k

k = -.32

But...now what?

y = (-.32)x^2 + bx + c

?
• Mar 5th 2010, 06:33 PM
Bacterius
Well, as Skeeter said, that means that your curve can be modelled by the equation :

$y = 0.32x(x - 10)$

By expanding :

$y = 0.32x^2 - 3.2x$

(there is no constant $c$ for this quadratic)