Chapter 9.7, Problem 50PPS

a.

To determine

To graph: The linear, quadratic, cubic and quartic.

Explanation of Solution

Given: The linear, quadratic, cubic and quartic equations.

For linear − Straight line: Maximum number of solution infinite.

  

For quadratic − straight line: Maximum two intersection point. So, two solutions.

  

For cubic - Straight line: Maximum three intersections points. So, three solutions.

  

For quartic − straight line: Maximum four intersection points. So, four solution.

  

b.

To determine

To complete: The table using graphs of part (a).

Answer to Problem 50PPS

  $\begin{array}{l}\text{Maximum number of Solutions for each system}\\ \begin{array}{cccc}\text{Type}& \text{Linear}& \text{quadratic}& \text{Cubic}\\ \text{Linear}& \infty & 2& 3\\ \text{Quadratic}& 2& 2& 3\\ \text{Cubic}& 3& 3& 3\\ \text{Quatic}& 4& 4& 4\end{array}\end{array}$

Explanation of Solution

Given: The table below:

  $\begin{array}{l}\text{Maximum number of Solutions for each system}\\ \begin{array}{cccc}\text{Type}& \text{Linear}& \text{quadratic}& \text{Cubic}\\ \text{Linear}& & & \\ \text{Quadratic}& & & \\ \text{Cubic}& & & \\ \text{Quatic}& & & \end{array}\end{array}$

Using graph complete the table to find maximum the number of intersection point on graphs.

  $\begin{array}{l}\text{Maximum number of Solutions for each system}\\ \begin{array}{cccc}\text{Type}& \text{Linear}& \text{quadratic}& \text{Cubic}\\ \text{Linear}& \infty & 2& 3\\ \text{Quadratic}& 2& 2& 3\\ \text{Cubic}& 3& 3& 3\\ \text{Quatic}& 4& 4& 4\end{array}\end{array}$

c.

To determine

To graph: The intersection of linear, quadratic, cubic and quartic with parabola.

Explanation of Solution

Given: The linear, quadratic, cubic and quartic.

Below are four graphs intersection of quadratic with linear, quadratic, cubic and quartic.

  

d.

To determine

To complete: The table using graphs of part (b).

Answer to Problem 50PPS

  $\begin{array}{l}\text{Maximum number of Solutions for each system}\\ \begin{array}{cccc}\text{Type}& \text{Linear}& \text{quadratic}& \text{Cubic}\\ \text{Linear}& \infty & 2& 3\\ \text{Quadratic}& 2& 2& 3\\ \text{Cubic}& 3& 3& 3\\ \text{Quatic}& 4& 4& 4\end{array}\end{array}$

Explanation of Solution

Given: The table below:

  $\begin{array}{l}\text{Maximum number of Solutions for each system}\\ \begin{array}{cccc}\text{Type}& \text{Linear}& \text{quadratic}& \text{Cubic}\\ \text{Linear}& & & \\ \text{Quadratic}& & & \\ \text{Cubic}& & & \\ \text{Quatic}& & & \end{array}\end{array}$

Using graph complete the table to find maximum the number of intersection point on graphs.

  $\begin{array}{l}\text{Maximum number of Solutions for each system}\\ \begin{array}{cccc}\text{Type}& \text{Linear}& \text{quadratic}& \text{Cubic}\\ \text{Linear}& \infty & 2& 3\\ \text{Quadratic}& 2& 2& 3\\ \text{Cubic}& 3& 3& 3\\ \text{Quatic}& 4& 4& 4\end{array}\end{array}$