Which of the following could represent the graph of $y = -x^2 + 1$?
A - HSC - SSCE Mathematics Standard - Question 1 - 2020 - Paper 1
Question 1
Which of the following could represent the graph of $y = -x^2 + 1$?
A.
B.
C.
D.
Worked Solution & Example Answer:Which of the following could represent the graph of $y = -x^2 + 1$?
A - HSC - SSCE Mathematics Standard - Question 1 - 2020 - Paper 1
Step 1
Identify the quadratic function
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Answer
The given function is y=−x2+1, which is a downward-opening parabola with its vertex at the point (0, 1).
Step 2
Determine the vertex
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Answer
The vertex of the parabola can be derived from its equation. The vertex form of a quadratic function is y=a(x−h)2+k, where (h, k) is the vertex. In this case, the vertex is at (0, 1).
Step 3
Analyze the graph options
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Answer
We need to check all four graph options.
Option A does not represent a parabola.
Option B is an upward-opening curve, which doesn't match our function.
Option C shows a downward-opening parabola with a vertex at (0, 1), which fits with our function.
Option D shows an incorrect placement of the vertex.
Step 4
Select the correct graph
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Answer
Thus, the answer is C, as it correctly represents the graph of the function y=−x2+1.
