Find expressions for the quadratic functions whose graphs are shown.

f(x) =

g(x) =

http://www.webassign.net/scalcet/1-2-8.gif

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- Sep 9th 2009, 02:00 PMkyleu03quadratic functions
Find expressions for the quadratic functions whose graphs are shown.

f(x) =

g(x) =

http://www.webassign.net/scalcet/1-2-8.gif - Sep 9th 2009, 02:07 PMJameson
The normal form we work with discussing parabolas is $\displaystyle y=ax^2+bx+c$. You need to find what "a" and "c" are. You have two variables and two points to work with. That's enough to solve for each variable.

Make sense?

EDIT: Big mistake, my apologies. See below post to clarify. - Sep 9th 2009, 03:38 PMkyleu03
that works for g(x) but not f(x) becuase there is only one point (the 3,0 doesnt seem to work)

- Sep 9th 2009, 03:52 PMJameson
- Sep 9th 2009, 03:56 PMkyleu03
- Sep 9th 2009, 04:04 PMJameson
I made a big mistake, my apologies. The normal form should be $\displaystyle y=ax^2+bx+c$. There are three variables to solve for, a b and c. So you need three pairs of (x,y) points to be able to solve for a b and c. G(x) gives you three points but for F(x) you have to use the fact that the parabola is symmetrical to get a third point.

Since you have the point (4,2) you can deduce that there is also the point (2,2) on the graph. Now you plug in your three (x,y) pairs into the equation I wrote above and solve for your a, b and c. - Sep 9th 2009, 04:51 PM11rdc11
- Sep 9th 2009, 05:07 PMJameson
- Sep 9th 2009, 05:09 PM11rdc11