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System of quadratic-quadratic equations
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System of quadratic-quadratic equations
The solutions to a system of equations are the points of intersection of the lines. For a system with two quadratic equations, there are 4 cases to consider: 2 solutions, 1 solution, no solutions, and infinite solutions.
Basic Concepts: System of linear-quadratic equations, Solving quadratic equations by factoring, Solving quadratic equations using the quadratic formula
Related Concepts: Graphing linear inequalities in two variables, Graphing systems of linear inequalities, Graphing quadratic inequalities in two variables, Graphing systems of quadratic inequalities
Lessons
- Introduction• The solutions to a system of equations are the points of intersection of the graphs.
• For a system consisting of two quadratic equations:
quadratic equation: y=ax2+bx+c
quadratic equation: y=dx2+ex+f
There are 4 cases to consider:case 1: 2 solutions case 2: 1 solution case 3: no solutions case 4: infinite solutions
- 1.Case 1: System with 2 Solutions
Solve the system, then verify the solutions graphically:
y=x2−6x+5
y=−2x2+9x−7
- 2.Case 2: System with 1 Solution
Solve the system, then verify the solutions graphically:
y=2x2+6x+7
y=−x2+4
- 3.Case 3: System with No Solutions
Solve the system, then verify the solutions graphically:
y=−x2+6x−10
y=2x2+6x+5
- 4.Case 4: System with Infinite Solutions
Solve the system, then verify the solutions graphically:
x2−4x−y+3=0
5y−5x2+20x−15=0