Card 1 of 20
EasyStudy card 1
Prompt
What do solutions of a system represent graphically?
Answer
Intersection points of the graphs.
MathChapter 11: Quadratic Functions
Flashcards
Solving Systems Consisting of Linear and Quadratic Equations Flashcards
Twenty cards on substitution, intersections, tangency, discriminants, and verification.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
How many real intersections can a line and parabola have?
Answer
Zero, one, or two.
Card 3 of 20
EasyStudy card 3
Prompt
What does one line-parabola intersection usually represent?
Answer
A tangent case with one repeated input solution.
Card 4 of 20
EasyStudy card 4
Prompt
What is the first algebraic step when both equations equal \(y\)?
Answer
Set their right-hand expressions equal.
Card 5 of 20
EasyStudy card 5
Prompt
What follows substitution in a line-quadratic system?
Answer
Solve the resulting one-variable quadratic.
Card 6 of 20
EasyStudy card 6
Prompt
Why are input roots not complete system answers?
Answer
Each root needs its corresponding output coordinate.
Card 7 of 20
EasyStudy card 7
Prompt
How do you verify an ordered pair?
Answer
Substitute it into both original equations.
Card 8 of 20
MediumStudy card 8
Prompt
When does a reduced discriminant show zero intersections?
Answer
When \(D<0\).
Card 9 of 20
MediumStudy card 9
Prompt
When does a reduced discriminant show tangency?
Answer
When \(D=0\).
Card 10 of 20
MediumStudy card 10
Prompt
When does a reduced discriminant show two intersections?
Answer
When \(D>0\).
Card 11 of 20
MediumStudy card 11
Prompt
How do you solve a quadratic-quadratic system at this level?
Answer
Set the functions equal, solve the reduced equation, then recover outputs.
Card 12 of 20
MediumStudy card 12
Prompt
Can two quadratic graphs have more than two intersections in general?
Answer
Yes, but Chapter 11 keeps the algebra at a source-aligned manageable level.
Card 13 of 20
MediumStudy card 13
Prompt
What is the horizontal-line tangency shortcut?
Answer
Its output equals the parabola's vertex output.
Card 14 of 20
MediumStudy card 14
Prompt
What is the graph consistency rule?
Answer
Every marked intersection must satisfy every displayed equation.
Card 15 of 20
MediumStudy card 15
Prompt
What is the omitted-root trap?
Answer
A quadratic can yield two inputs, and both must be checked.
Card 16 of 20
MediumStudy card 16
Prompt
When should contextual restrictions be applied?
Answer
After finding and algebraically verifying all candidate ordered pairs.
Card 17 of 20
HardStudy card 17
Prompt
Solve \(y=x^2-1\) and \(y=x+1\).
Answer
\((-1,0)\) and \((2,3)\).
Card 18 of 20
HardStudy card 18
Prompt
What discriminant do you use for a system?
Answer
The discriminant of the one-variable quadratic obtained after substitution.
Card 19 of 20
HardStudy card 19
Prompt
Why can a point on only one graph not solve a system?
Answer
A solution must make both equations true simultaneously.
Card 20 of 20
HardStudy card 20
Prompt
What is the safest final systems check?
Answer
Substitute every ordered pair into both original equations and compare with the graph.
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