Question

The graphs below have the same shape. What is the equation of the blue

Answer 1

Answer: The correct option is B.

Explanation:

From the given figure it is noticed that the parent function is,

$f(x)=x^2$

The graph of f(x) shifts 5 units right.

The transformation is defined as,

$g(x)=f(x+a)+b$

Where, a shows the horizontal shifts and b shows the vertical shift.

If a<0 then the graph of f(x) shifts right side by a units and if a>0 then the graph of f(x) shifts left side by a units.

If b<0 then the graph of f(x) shifts downward by b units and if b>0 then the graph of f(x) shifts upward by b units.

Since the graph of parent function is shifts only right side by 5 units, therefore

$g(x)=f(x-5)+0$

Since $f(x)=x^2$

$g(x)=(x+5)^2$

Thus, the correct option is B.

The function in option A represents the left shift of f(x) by 5 units.  The option C represents the downward shift of f(x) by 5 units. The option D represents the upward shift of f(x) by 5 units.

Answer 2

Using a graph tool
see the attache figure

the answer is the option B
g(x)=(x-5)²