Question

Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Check all that apply.

A.The graph of f(x) = x2 is shifted up 25 units.
B.The graph of f(x) = x2 is shifted up 50 units.
C.The graph of f(x) = x2 is shifted down 950 units.
D.The graph of f(x) = x2 is shifted left 10 units.
E.The graph of f(x) = x2 is shifted right 10 units.
F.The graph of f(x) = x2 is reflected over the x-axis.

Answer 1

B D E

Explanation:

2 4 5

Answer 2

Consider the function
`g(x) =-5x^2 + 100x- 450`. First you need to simplify it by expressing the perfect square:

`g(x) =-5x^2 + 100x- 450=-5(x^2-20x+90)=-5(x^2-2\cdot x\cdot 10+10^2-10^2+90)=-5((x-10)^2-100+90)=-5(x-10)^2+50.`

So you get
`g(x) =-5(x-10)^2+50`.

Now you can consider all transformations that have been applied to the graph of
`f(x) = x^2` to produce the graph of g(x):

1. translate the graph of the function
   `f(x)` right 10 units - this transformation gives you the graph of the function
   `f_1(x)=(x-10)^2`;
2. reflect graph of the function
   `f_1(x)` about the x-axis. This transformation gives you the graph of the function
   `f_2(x)=-(x-10)^2`;
3. stretch the graph of the function
   `f_2(x)` in the y-direction by multiplying the whole function by 5, then you get the function
   `f_3(x)=-5(x-10)^2`;
4. translate the graph of the function
   `f_3(x)` up 50 units, then you get the graph of the function
   `g(x) =-5(x-10)^2+50`.

From the algorithm above you can conclude that choices B, E and F are correct.