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The picture below shows the top section of the Spanish Arch in Galway city - Junior Cycle Mathematics - Question 8 - 2014
Question 8
The picture below shows the top section of the Spanish Arch in Galway city. George wants to see if the arch can be described by a function. He puts a co-ordinate gri... show full transcript
Worked Solution & Example Answer:The picture below shows the top section of the Spanish Arch in Galway city - Junior Cycle Mathematics - Question 8 - 2014
Step 1
Complete the table below to show the value of y for each of the given values of x.
Answer
After analyzing the graph, the y-values corresponding to the provided x-values can be estimated as follows:
- For x = -3, y ≈ 1.6
- For x = -2, y ≈ 2.9
- For x = -1, y ≈ 3.4
- For x = 0, y ≈ 3.7
- For x = 1, y ≈ 3.4
- For x = 2, y ≈ 2.9
- For x = 3, y ≈ 1.6
The completed table is:
| x | y |
|---|---|
| -3 | 1.6 |
| -2 | 2.9 |
| -1 | 3.4 |
| 0 | 3.7 |
| 1 | 3.4 |
| 2 | 2.9 |
| 3 | 1.6 |
Step 2
Is it possible to represent this section of the Spanish Arch by a quadratic function? Give a reason for your answer.
Answer
No, it is not possible to represent this arch by a quadratic function. A quadratic function describes a parabola, which is symmetric about its vertex. For this arch, the highest point (y-value) is not at x = 0, which means it cannot be represented by a quadratic function that is symmetric about the y-axis. The observed values in the table indicate that as x approaches -3 or 3, the y-values become equal (1.6), but the arch's shape varies non-symmetrically as x increases, showing it cannot conform to the shape of a quadratic.