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Identify Parent Function of Quadratic Equation y=(x+2)(x-2)
Published on March 30, 2026
Functions
This problem asks to identify the graph of the parent function y = x^2 from a set of transformations of the quadratic equation y = (x+2)(x-2). The parent function has its vertex at the origin (0, 0).
Question
Answer
Here is the step-by-step solution to find the graph representing the parent function of
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Identify the given function:
The given function is. -
Determine the general form of the parent function:
The functionis a quadratic function because multiplying the factors results in a term with : The parent function for a parabola is. -
Analyze the relationship between the given function and the parent function:
The general form of a transformed quadratic function based on the parent functionis , where is the vertex. Let’s rewrite the given functionin vertex form. We can see that , , and . This means the graph ofis the parent function shifted 4 units down. The vertex of this function is . -
Identify the properties of the parent function (
):
The parent functionis a parabola that opens upwards and has its vertex at the origin .
Key points oninclude: - Vertex:
- Points:
, , , , etc.
- Vertex:
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Compare the parent function’s graph with the given options:
We are looking for the graph that represents the parent function, which must have its vertex at the origin and open upwards. - Graph A: The vertex is at
and it opens upwards. This represents . - Graph B: The vertex is at
and it opens upwards. This matches the parent function . - Graph C: The vertex is at
and it opens upwards. This represents . - Graph D: The parabola opens downwards (the coefficient of
is negative). This represents a reflection across the x-axis, e.g., .
- Graph A: The vertex is at
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Conclusion:
Graph B represents the parent function.
The graph that represents the PARENT FUNCTION of