Transformation of Functions · Exercise 16

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.

Fill in the blanks:
ⓐ If c > 0, the graph of $y=f\left(x\right)+c$ is obtained by shifting the graph of $y=f\left(x\right)$ to the ________ a distance of c units. The graph of $y=f\left(x\right)–c$ is obtained by shifting the graph of $y=f\left(x\right)$ to the ________ a distance of c units.
ⓑ If c > 0, the graph of $y=f\left(x\right)–c$ is obtained by shifting the graph of $y=f\left(x\right)$ to the ________ a distance of c units. The graph of $y=f\left(x\right)+c$ is obtained by shifting the graph of $y=f\left(x\right)$ to the ________ a distance of c units.

This exercise has fill-in blanks from its source book and no answer key.

OpenStax, Algebra and Trigonometry 2e · §3.5 Transformation of Functions · Exercise 16