The areas of the parallelograms can be compared as: A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
<h3>What is a parallelogram?</h3>A parallelogram refers to a geometrical shape and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
<h3>How to calculate the area of a triangle?</h3>Mathematically, the area of a triangle can be calculated by using this formula:
Area = ½ × b × h
Where:
Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
Next, we would determine the area of the two parallelograms as follows:
Area of parallelogram 1 = Area of red-rectangular figure - Area of triangle A - Area of triangle B - Area of triangle C - Area of triangle D.
Substituting the given parameters into the formula, we have;
Area of parallelogram 1 = (6 × 6) - (½ × 4 × 2) - (½ × 2 × 4)- (½ × 4 × 2) - (½ × 2 × 4)
Area of parallelogram 1 = 36 - 4 - 4 - 4 - 4
Area of parallelogram 1 = 36 - 16
Area of parallelogram 1 = 20 units².
For parallelogram 2, we have:
Area of parallelogram 2 = Area of blue-rectangular figure - Area of triangle P - Area of triangle Q - Area of triangle R - Area of triangle S.
Substituting the given parameters into the formula, we have;
Area of parallelogram 2 = (8 × 4) - (½ × 2 × 2) - (½ × 6 × 2)- (½ × 2 × 2) - (½ × 2 × 6)
Area of parallelogram 2 = 32 - 2 - 6 - 2 - 6
Area of parallelogram 2 = 32 - 16
Area of parallelogram 2 = 16 units².
Difference = Area of parallelogram 1 - Area of parallelogram 2
Difference = 20 - 16
Difference = 4 units².
In conclusion, we can infer and logically deduce that the area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
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Answer:
,
Step-by-step explanation:
The function of the graph can be written in the vertex form as
, where V(h,k)=V(2,4) is the vertex of the quadratic function.
We substitute the value to obtain;
,
The point (5,1) lies on the graph so we use it to determine the value of a.
,
,
,
The required equation is
,