Question

Y=f(1/3x) & find new coordinates

Answer 1

A(-3,0)

B(6,1)

C(15,0)

Explanation:

To find the three new coordinates A,B,C we have to find out the equation of the original curve y=f(x) which is shown in the figure. We find that equation by using the turning point (2,1) which is point B and take any other point either A or C which intercept's the x-axis, i took C. We put both these points into the completing square formula of the curve.

`y=a(x-h)^2+k`

where (h,k) are the turning points (2,1) respectively and C (5,0) corresponds to (x,y)

so the equations becomes

`0=a(5-2)^2+1\\0=a(3)^2+1\\0=9a+1\\-1=9a\\a=(-1)/(9)`

So our equation y=f(x) becomes

`y=-((x-2)^2)/(9)+1`

now for

`y=f((x)/(3) )`

we replace the x in the original equation above with x/3 which changes the equation to

`f((x)/(3) )=-(((x)/(3)-2)^2)/(9) +1`

and now we sketch the curve we have our hints for the new points A,B,C our hint is that the original points A and C are the x-intercepts so the new A and C lets name them A' and C' must be the x-intercepts as well and B is the turning point of y=f(x) so the new point B' must be the turning point of y=f(x/3)

so we simply sketch the curve y=f(x/3) use an online graph plotter if you know how to sketch it to save time or if you don't know you can ask me and i'll teach you cause learning to sketch isn't in the question so furthermore we sketch the curve i attached the figure in an image you check it out and the new points as well.