(a) Look at the picture below: we started with the square ABCD, with side length , and we built the rectangle AEFG such that
(b) Since the dimensions of AEFG are and
, its area will be the product of its dimensions:
(c) The area is a function of the side length
:
(d) Since is a polynomial with degree 2, it represents a parabola. In order to find the x intercept, we must set
:
Similarly, in order to find the y intercept, we must set :
The x-coordinate of the vertex is given by
And its y coordinate is given by
The line of symmetry is the vertical line passing through the vertex, so it must be
(see the second picture for the graph)
(e) The graph opens upward. We knew that from the equation, because given a parabola
its graph will open upwards if , downwards if
. In your case,
, so it's positive and the parabola opens upwards.
