alleryStart learning →How does the graph of f(x) = x squared minus 5 compare with the graph of f(x) = x squared?
- It sits 5 units higher
- It is 5 times narrower
- It is 5 times wider
- It sits 5 units lower
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Correct answer: D. It sits 5 units lower
1. Adding a constant to the whole rule changes every output by that amount.
2. Here the constant is negative 5, so every output drops by 5.
3. The graph therefore sits 5 units lower than the basic parabola.
4. The shape is unchanged, since nothing has been multiplied by a stretch factor.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.7 Graph Quadratic Functions Using Transformations_