How do I do this math questions

Actually Welcome to the Concept of the Area and Volumes.

First we divide this figure in to two shapes , that are Triangle and Rectangle and apply their area formulae.

Total Area = Area of triangle + Area of Rectangle.

Area of triangle = 0.5*b*h

= 0.5*4*5

= 10 sq. units.

---> Area of Rectangle = l*b

= 7*5= 35 sq. units

thus the total area of the Shape is

= 35 + 10= 45 sq. units

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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