write the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5).

Step-by-step explanation:

We are given that  endpoints of a diameter at the points (7,2) and (-9,5).

Center of the circle is the mid point of diameter

So, first find the mid point of diameter

Formula :

Substitute the values in formula

So, center of circle = (h,k )=(-1,3.5)

To find length of diameter :

Length of radius = r =

Standard form of the equation of the circle :

(h,k )=(-1,3.5)

Equation of the circle :

Equation of the circle :

Hence  the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5) is  

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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step-by-step explanation: