### Home > CCA2 > Chapter 8 > Lesson 8.2.3 > Problem8-105

8-105.

Make a sketch of a graph $p(x)$ so that $p(x) = 0$ would have the indicated number and type of solutions.

1. $5$ real solutions

Your graph should have five $x$-intercepts.

1. $3$ real and $2$ complex

Draw a graph with three $x$-intercepts that when shifted vertically would have five $x$-intercepts.

1. $4$ complex

Draw a graph with no $x$-intercepts. But, when it is shifted down it should have four $x$-intercepts.

1. $4$ complex and $2$ real

1. For parts (a) through (d), what is the lowest degree each function could have?

The degree needs to be at least as high as the number of solutions.