a.
To Draw: The number of points of intersection linear function and a quadratic function have.
Given:
Linear function and a Quadratic function
Explanation:
If linear function and quadratic function intersect, one, two, or no solution exists.
The system has one solution, if a line intersects the quadratic function at one point.
The graphical representation is:
  
The system has two solutions, if a line intersects the quadratic function at two points.
The graphical representation is:
  
The system has no solution if a linear function does not intersect the quadratic function.
The graphical representation is:
  
b.
To Draw: The number of points of intersection two quadratic function have.
Given:
Two Quadratic functions
Explanation:
One, two, or no solutions are possible for the system of quadratic equations.
One solution exists if the two quadratic equations intersect at one point.
The graphical representation is:
  
There are two solutions to a system of quadratic equations if the two quadratic equations intersect at two points.
The graphical representation is:
  
When the two quadratic equations do not intersect, then there is no solution to the system of quadratic equations.
The graphical representation is:
  
c.
To Draw: The quadratic function and an absolute value function
Given:
Graph
Transform one of the graphs slightly to increase the number of intersections.
Explanation:
There may be one, two, three, four, or no solution to the intersection of a quadratic function and an absolute value function.
The graph shows one solution:
  
The below graph shows two solutions:
  
The below graph shows three solutions:
  
The below graph shows three solutions:
  
The below graph shows zero solutions:
  
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education