Question

the graph of f(x) shown below has the same shape as the graph of g(x)=x^2 but is shifted down 5 units and to the left 4 units (thank you)

Answer 1

D.
`F(x)=(x+4)^2-5`

Explanation:

The parent function is
`G(x)=x^2`.

This function has its vertex at the origin (0,0).

When this function is shifted down 5 units and to the left 4 units, then its new vertex will be at (-4,-5)

The vertex form of the equation is given by;

`F(x)=a(x-h)^2+k` where (h,k)=(-4,-5) is the vertex and a=1 because of the parent function.

Hence its equation is

`F(x)=(x+4)^2-5`

Answer 2

Option C

Explanation:

A function g(x) = x² has been given as the parent function.

This function then shifted 5 units down.

Translated function formed will be f(x) = x² - 5

Further this graph has been shifted 4 units to the left then the function will become

f(x) = [x - (-4)]² - 5

f(x) = (x + 4)² - 5

Therefore, option C is the answer.