Find the area of the shape above ?

Area of triangle = A(t) = 1/2(base x height)

Area of square = A(s) = base x height

A(s) = 2 x 2 = 4

2(A(s)) = 2(1/2(2)(2) = 2(1/2(4)) = 2(2) = 4

Add the two areas together

4 + 4 = 8

8 units² is your answer

The shape is a polygon called a trapezoid. The trapezoid has two parallel sides. The bottom parallel side measures 2 units. The upper parallel side measures 2 + 2 + 2 = 6 units. The perpendicular to the bases is the height; it measures 2 units.

Area of trapezoid:

A = (B + b)h/2

where B = length of one base

b = length of other base

h = length of height

A = (6 + 2)(2)/2

A = 8

8 units^2

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