Question

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

Answer 1

B.
`g(x)=(x-2)^2+1`

Explanation:

The equation of the red graph is
`f(x)=x^2`.

The blue graph has its vertex at (2,1)

Hence its equation is of the form;

`g(x)=a(x-2)^2+1`

This graph has y-intercept (0,5).

`5=a(0-2)^2+1`

`5-1=a(-2)^2`

`4=4a`

`1=a`

The blue graph therefore has equation;

`g(x)=(x-2)^2+1`

Answer 2

Answer: OPTION B

Explanation:

The red graph shows the parent function of a quadratic function (which is the simplest form of a quadratic function), whose vertex is at the origin.

The function g(x) is the result of shift the parent function 2 units to the right and shift it 1 unit up.

Therefore, keeping the above on mind you have that the transformation has the following form:

`g(x)=(x-h)^2+k`

Where the horizontal shift depends on the value of h and the vertical shift depends on the value of k.

Therefore, you obtain the function:

`g(x)=(x-2)^2+1`