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VCE Stuff => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematics => Topic started by: nina_rox on August 29, 2010, 03:31:27 pm

Title: Help with Methods unit 1!
Post by: nina_rox on August 29, 2010, 03:31:27 pm: hey i'm nina and i'm a year 10 student in melbourne.
I need help with a question in the methods textbook under the chapter "Functions, Relations and Transformations."
The subheading is "Miscellaneous exercises"
Here is the question:
Find two quadratics functions f and g such that f(1)=0 and g(1)=0 and f(0)=10, g(0)=10 and both have a maximum of 18

Hope you can help!

Thanks for your help in advance! :)
Title: Re: Help with Methods unit 1!
Post by: nina_rox on August 29, 2010, 03:31:57 pm: oops i posted on two places...
Title: Re: Help with Methods unit 1!
Post by: kamil9876 on August 29, 2010, 07:13:23 pm: f(1)=0 means that (x-1) is a factor so you can write f(x) as:

$f(x)=a(x-1)(x-c)$

by plugging in $f(0)=10$ you know that

$ac=10$ [1]

Now the maximum occurs at the $x$ value that is the midpoint of the two roots, hence the maximum occurs at $\frac{c+1}{2}$

So you have:
$<br />f(\frac{c+1}{2})=18$ [2]

[1] and [2] can now be solved.