Chapter 1.1, Problem 46E

To determine

To graph: The parent quadratic function and a quadratic function that has no $x-\mathrm{int}ercepts$ and then to describe the transformations of the parent function.

Answer to Problem 46E

If a function is shifted up by some factor from the parent quadratic function, then it has no x-intercepts.

Explanation of Solution

Given information: Quadratic functions are to be graphed.

Graph:

  

Interpretation:

The function $g(x)=4x^2+2$ is graphed in blue color, it is vertically stretched by a factor of $4$ and has a vertical translation of $2units$ upward with respect to the parent function $f(x)=x^2$ . Also, the function $g$ has no x-intercepts.

Thus, if a function is shifted up by some factor from the parent quadratic function, then it has no x-intercepts.