What is the vertex of the graph of f(x)=|x-13| +11?

Hello!

Like quadratic function, absolute value functions have a vertex form. Its vertex form is: f(x) = a|x - h| + k. In this formula, a is the vertical shift/compression, h is the horizontal shift, and k is the vertical shift. (h, k) is the vertex.

In this equation, a is 1, so there is no vertical stretch/compression. Also, h has a value of 13, and k has a value of 11.

Therefore, the vertex of f(x) is (13, 11).

me i beg !

step-by-step explanation:

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.