What is the effect on the graph of the function f(x)=x^2 when f(x) is changed to f(x)+9

Given:

The function is

This function is changed to f(x)+9.

To find:

The effect on the graph of the function.

Solution:

The translation is defined as

               .... (1)

Where, b is vertical shift.   If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The new function is

          ...(2)

From (1) and (2), we get

So, the graph of f(x) shifts 9 units up as shown in the below graph.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.