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The graphic on the right shows an image from the 'Angry Birds' computer game - Leaving Cert DCG - Question A-2 - 2015
Question A-2
The graphic on the right shows an image from the 'Angry Birds' computer game. The curve is in the shape of a parabola. The drawing below shows a portion of a parabol... show full transcript
Worked Solution & Example Answer:The graphic on the right shows an image from the 'Angry Birds' computer game - Leaving Cert DCG - Question A-2 - 2015
Step 1
Locate the remaining points on the parabola.
Answer
To locate the remaining points on the parabola, we follow these steps:
- Complete division of CB: The line segment CB can be divided symmetrically. Since point V is the vertex, the x-coordinates of C and B will be equidistant from V.
- Division of CV: The segment CV can be divided into two equal parts, resulting in a midpoint that represents the focus of the parabola, which influences its curvature.
- Construction lines (2 sets): Draw horizontal and vertical construction lines through points C and A, and lines through points D and B to define the full extent of the parabola. Setting up coordinates such as (2,2) allows for accurate plotting.
- Identify points on LHS of curve: By applying the properties of parabolas, we can identify additional points on the left-hand side by choosing symmetrical x-values from the vertex. For example, if V is at (0,0), points like (-1,1) and (-2,4) can be used.
- Points on RHS of curve: Similarly, find points on the right-hand side of the curve. Using the same x-values but applying them positively (1,1) and (2,4) will help complete the curve structure.
Step 2
Draw the complete parabola.
Answer
To draw the complete parabola, follow these instructions:
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Complete the curve on the LHS: Using the identified points and construction lines from the previous step, sketch a smooth curve on the left side of the vertex V, ensuring it reflects the typical 'U' shape of a parabola.
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Complete the curve on the RHS: Similarly, mirror the left curve on the right side using the identified points to ensure symmetry.
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Ensure presentation accuracy: Make sure the drawing is clear, with the parabola gracefully connecting both sides. Label points A, B, C, D, and V for easy reference, with dashed lines for construction to differentiate them from the final curve.