Transformation of Functions · Exercise 15

The graphs of quadratic functions are called parabolas. Use a graphing program to graph each of the following quadratic functions. For each graph find the vertex (the minimum or maximum value) of the parabola and list its coordinates. Most importantly use the patterns observed to answer each of the given questions.

Answer each of the following based on the changes you saw in the graphs above.
ⓐ Based on your observations from the previous graphs, what are the coordinates of the vertex of the parabola $f\left(x\right)={\left(x+200\right)}^2-67$? Do not attempt to graph!
ⓑ Based on your observations from the previous graphs, what are the coordinates of the vertex of the parabola $f\left(x\right)=12{\left(x+6\right)}^2+111$? Do not attempt to graph!

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Algebra and Trigonometry 2e · §3.5 Transformation of Functions · Exercise 15