The equation y^2+8y−x+18=0 represents a parabola. Drag and drop the expressions into the boxes in the equation to rewrite the equation of this parabola in standard form.

x= ( )^2 + ___

The equation of parabola is standard form is

Step-by-step explanation:

Given equation of parabola is,

In order to find the equation of parabola in standard form, eliminate x from left side of equation and use completing square method to find the equation.

First step is to add x on both side of equation.

Rewriting,

Now applying completing square method as follows.

Following are the steps for calculation of this method.

Find the last term of above equation by using below formula,

Now coefficient of y is 8.

Simplifying,

Second step is to add and subtract the last term.

Rewriting,

Since

Using above formula,

Therefore, the equation of parabola in standard form is

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.

2x^2+5x+17

your welcome. : )