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The graphic below shows a water fountain in Sweden - Leaving Cert DCG - Question A-4 - 2013
Question A-4
The graphic below shows a water fountain in Sweden. The fountain is in the shape of a parabola. The drawing on the right shows a portion of a parabola inscribed in ... show full transcript
Worked Solution & Example Answer:The graphic below shows a water fountain in Sweden - Leaving Cert DCG - Question A-4 - 2013
Step 1
Locate the remaining points on the parabola.
Answer
To locate the remaining points on the parabola, we first recognize that the vertex (V) is located at the highest point of the fountain.
Given the shape of the parabola, we observe that it opens upwards. The remaining points can be identified by selecting equal distances from the vertex V to find points A and D on the left and right.
By applying the property of parabolas, we can also identify corresponding points along the y-axis (directrix).
For instance, if V is at (0, h), we consider points (±a, b) on the curve where 'a' is the horizontal distance from the vertex to points A and D.
Calculating values, we can plot corresponding points along the line CD in the rectangle.
Step 2
Draw the complete parabola.
Answer
To draw the complete parabola, we start from the identified points on the curve.
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Using a ruler, connect points A and D to point V through a smooth arc, ensuring that the curve aligns with the identified parabolic shape.
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Ensure the drawn curve is symmetrical and maintains the properties of a parabolic arc, reflecting the upward opening.
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Add dashed or solid lines to denote the parabola clearly, confirming it meets points B and A along the rectangle’s boundaries, ensuring the entrance and exit for the fountain water are correctly illustrated.
Make any adjustments required to ensure the curve smoothly transitions through these points.