The function g(x) varies directly with x^2 and g(x)=50 when x=10

Question

Need help with solving and then graphing this question because I don't understand how to do it at all.
UPDATE:
It's a multiple choice question with 4 graphs, the first one has the usual U shaped line but the main points it's showing is (-3,18), (-2,8), (-1,2), (1,2), (2,8), and (3,18). The second one is the same as the first, but the U shape is not only wider, but the main points for it is (-2,2), (-3,4.5), (-1,0.5), (1,0.5), (3,4.5), and (2,2). The third is like the first one, normal U shaped line and the main points for it are (-2,12), (-1,3), (2,12), and (1,3). The last graph is like the second one, wider shaped U line, with the main points of (-3,3), (-2, 4/3), (-1,1/3), (1,1/3), (2,4/3), and (3,3). I am so lost on this. 

Answer 1

Rhianna,

 

g(x) varying directly with x² means that g(x) = k x² where k is some constant that we don't know.  We can find that out by putting in the set that we know. (10,50)    That means 50 = k 10²   Solve that for k and put it into g(x) = k x²   That is the answer for the equation, and you can graph it.  It's a parabola and you can find some points and graph it.

You can do it!

Mary

Answer 2

call g(x) "y" for ease of working.

 

So y is directly proportional to x² meaning:

y = kx²  where k is the constant of proportion

 

50 = k(10)²

50 = 100k

50/100 = k

1/2 = k

 

Your function is:  g(x) = (1/2)x²

 

This will be a parabola opening upward from (0, 0)

 

x      (1/2)x²

--------------

-4      8

-2      2

0       0

2       2

4       8

 

Plot the points and draw the graph realizing that both

sides will continue upward to infinity.