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Transformation of the graph of a function

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See file for an example from textbook.
I plugged in x^2 + 6x + 10 into my calculator and got the required graph and the answer of -3 units parallel to the x-axis.
But how does one come to this answer of -3units 'manually' without using a calculator?
Thank you.

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Solution Summary

Detailed step by step solution is provided. It also explains how to find vertex of quadratic function without using calculator.

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Solution:

We can write it as

g = x^2 + 6x + 10

g = x^2 + 6x + 9 + 1

g = (x + 3)^2 + 1

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Solution provided by:
Sandhya Sharma, MSc
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  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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