Question

The graph of Fx), shown below, resembles the graph of G(X) = x?, but it has

Answer 1

Answer:

$y=\left(x-a\right)^{2\ }+b$

$y=\left(x-2\right)^{2\ }+2$

Step-by-step explanation:

Since we are not given any options so we will start with the general case.

The equation of such a graph can be modeled as

$y = x^{2}$

This graph is symmetrical around the origin, but in the attached diagram, the graph is shifted in the x-axis as well as in the y-axis,

$y=\left(x-a\right)^{2\ }$

Where the variable a shifts the graph to the right of x-axis when a is positive, when it is negative it shifts the graph to the left that is negative x-axis.

$y=\left(x-a\right)^{2\ }+b$

The variable b shifts the graph upward in the positive y-axis when b is positive, when it is negative it shifts the graph to the bottom that is negative y-axis.

Since in the attached diagram, the graph is in the positive x-axis and y-axis, therefore, a and b must be positive and can be estimated as

$y=\left(x-2\right)^{2\ }+2$

The graph of the above expression is attached and it looks very similar to the given graph.

Answer 2

Answer:

F(X) = $(x-2)^{2}$ + 2  

Step-by-step explanation:

Given G(X) = $x^{2}$

As we know it has  been changed somewhat to become F(X)

• Transformation 1:

Compare to the graph of G(X) the graph of F(X) has been vertical shift up to 2 units.  

=> our function of F(X) = $x^{2}$ + 2

• Transformation 2:  

Compare to the graph of G(X) the graph of F(X) has been horizontal shift to the right 2 units. For this investigation, you will compare the graph of

G = F(X-d) to G(X)

When d > 0 (when d is positive), the function is translated right |d| units or horizontal shift to the right 2 units

=> our function of F(X) = $(x-2)^{2}$ + 2  

Please have a look at the photo.

Hope it will find you well.