Question

Sketch the graph of y = x2 + 3 and y = |x| + 3 on the same axis in your notebook. List three ways that the two graphs are alike and three ways in which they differ. Be sure your graph is large enough to clearly show these differences. On another axis, sketch the graph of y = 2(x − 3)2 and y = 2|x − 3|. Also be prepared to explain how these two graphs compare.

Answer 1

Explanation

Let's first graph the two functions to find their similarities and differences:

similarities

- Both are even functions.

- Both have y-intercept at (0,3)

- None have an output value less than 3.

differences

- The quadratic function grows faster.

- In the (-1,1) interval the absolute value function outputs are greater than the quadratic ones.

- In the (-infinite,-1) and (1, infinite) intervals the quadratic function outputs are greater than the absolute value ones.