Which benchmark angles (multiples of 30 degrees or 40 degrees) are closest to the rotation angles below? a) 40 b) 140 c) 170 d) 220 e) 250 f) 310

The benchmark angles are angles that are used as references like- 30 degrees, 45 degrees, 60 degrees, etc.

The closest angles to given rotation angles are:

A- 40- closest to the multiple of 45 degrees.

B- 140- closest to the multiple of 45 degrees (135 degree).

C- 170- closest to the multiple of 30 degrees (closest to 180 degrees which is multiple of both 30 and 45 degrees).

D- 220 -closest to the multiple of 30 degrees (210 degree).

E- 250- closest to the multiple of 30 degrees (240 degree).

F- 310- closest to the multiple of 45 degrees (315 degree).

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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