The equation of a parabola is y=x^2–4x+13. Write the equation in vertex form. Simplify any fractions.

vertex form : y=(x-2)^2+9

Step-by-step explanation:

To convert a parabola from standard form y=x^2-4x+13 to vertex form, we complete the square.

first, complete the square using the x-terms, use the constant term to adjust and make a perfect square.

y=  x^2-4x+4   +  9

Factor the first three terms on the right-hand side.

y=(x-2)^2 + 9

the resulting express is then the vertex form, which means that

the vertex is at (x-2) = 0, x=2, and at y=9.  

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.

step-by-step explanation: