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The 3D graphic below shows Dublin's newest bridge, which is in the shape of a semi-parabola - Leaving Cert DCG - Question A-3 - 2011
Question A-3
The 3D graphic below shows Dublin's newest bridge, which is in the shape of a semi-parabola. The drawing on the right shows a rectangle ABCV with a portion of the p... show full transcript
Worked Solution & Example Answer:The 3D graphic below shows Dublin's newest bridge, which is in the shape of a semi-parabola - Leaving Cert DCG - Question A-3 - 2011
Step 1
Locate the remaining points on the curve and complete the semi-parabola.
Answer
To complete the semi-parabola, start by identifying points along the curve between points A and C that maintain the parabolic shape. Each point can be located by taking a consistent horizontal distance at various vertical intervals from point A to C. Use the general formula of the semi-parabola:, where (h, k) is the vertex of the parabola, to derive the required points. After determining these points, connect them smoothly to illustrate the semi-parabola.
Ensure that the vertex, point V, is clearly defined at the apex of the parabola.
Step 2
Draw the lower half of the parabola, representing the reflection in the water.
Answer
To create the lower half of the parabola, reflect the upper curve drawn in part (a) across the horizontal line that passes through point V and along line AV. This can be achieved by plotting the corresponding reflected points below line AV in the same horizontal positions as those on the upper curve. Ensure that the lower curve mirrors the upper curve symmetrically, creating a visually appealing representation of the reflection in the water.