Math 20-1 Ch.8 Linear-Quadratic and Quadratic-Quadratic Systems Solving Problems
Group Activity:
Students are randomly placed in groups of three. One person is given the paper copy of the questions and
the other two are given a mini-white board and dry erase markers to do rough work. Students may be
more creative and take risks when working with non-permanent materials.
Information on mini-white board can be found at
http://www.schoolsin.com/UVP-UV912G.html
Students must hand in group work at the end of class.
Individual students may obtain a digital copy of worksheet
and worked out solutions on our virtual classroom for Math 20-1.
If a group is struggling with a question, one member of the group may visit another group to get ideas. A
member of the receiving group will share their strategy for solving the question.
Near the end of class, students will be asked to visit other groups to verify solutions and discuss different
strategies.
Math 20-1 Ch.8 Linear-Quadratic and Quadratic-Quadratic Systems Solving Problems
1. Illustrate with a sketch a possible representation of a graphical solution for each.
Linear-Quadratic Systems
Label each line as tangent or secant to the parabola where appropriate.
No Solution
One Solution
Two Solutions
Quadratic-Quadratic Systems
No Solution
One Solution
Two Solutions
2. Only one of these systems, linear-quadratic or quadratic-quadratic, can have an infinite number of
solutions.
Name of System with Infinite
Sketch of possible
Example of System of
Solutions
representation of graphical
Equations with Infinite
solution
Solutions
3. Consider the following system of equations with two solutions.
x2  6 x  y  k  0
3x  y  k  0
a) Determine the value of k if a solution is  3, 2  .
b) Determine the coordinates of the second solution.
4. Consider the linear-quadratic system of equations to the right.
Determine the value(s) of k, if the system has
a) two solutions
y  x2  2x  3
yk
b) one solution
c) no solution
5. The sum of two integers is 21. Fifteen less than double the square of the smaller integer is equal to the
larger integer.
a) Model the information with a system in two variables.
Let x =
Let y =
Equations are:
b) Solve the system graphically to determine the value of the two integers.
c) Are both solutions possible? Explain.
6. A parabola’s vertex is at  4, 4  and one of its x-intercepts is at  6,0  . A second parabola’s vertex
2
is at 1, 9  and its y-intercept is at  0, 8 . Recall the vertex form of a quadratic y  a( x  p)  q
a) Determine the equations of the parabolas.
b) Algebraically solve the system of equations to determine the point(s) of intersection.
7. Consider the rectangular picture on the right. The perimeter is equal to y,
and the area is equal to 3y.
3x
a) Determine equations to represent the perimeter and area.
b) Solve the system of equations algebraically.
c) Are both solutions possible? Explain.
d) State the value of x, the perimeter, and the area.
x5