Family of Functions Question?(graph)

[cruisx]

Hi what's up, Can someone tell me what it means to create 3 sub functions that have both points of intersection with the x-axis in common? Like i understand if you are making a family with the same x-coord you could have something like this (4,0)(4,3)(4,5) but how do you graph a family with BOTH X-axis in common? What does this mean.

thanks.

 

[n!kofeyn]

Hi what's up, Can someone tell me what it means to create 3 sub functions that have both points of intersection with the x-axis in common? Like i understand if you are making a family with the same x-coord you could have something like this (4,0)(4,3)(4,5) but how do you graph a family with BOTH X-axis in common? What does this mean.

thanks.

Well those are just three points, only one of which lies on the x-axis. You want three functions that intersect at the same points along the x-axis. I can give you hints for two functions to start out with. See if you can augment them to create two separate families, where each family is a set of three functions that all have the same x-intercepts.

One function is f(x)=cos(x). The other is g(x)=x².

Also, I'm little confused by the bolded sentence above, so if I got the wrong idea, let me know.

 

[HallsofIvy]

If a graph of a quadratic function crosses the x-axis at x₀ and x₁, the function must be of the form y= a(x- x₀)(x- x_{1[/sup]). Choose three different values of a to get three different functions.}