Advanced Math / Systems Nonlinear Equations
Line-parabola intersections
A line-parabola system can be solved by setting the two expressions for $y$ equal. The resulting quadratic tells how many intersection points exist.
Least you need to know
- Two real roots give two intersections.
- One repeated root gives one intersection.
- No real roots give no real intersection points.
Key notation
- D — The discriminant $b^2-4ac$ of a quadratic
Worked example
If $x^2=2x+8$, then $x^2-2x-8=0$, or $(x-4)(x+2)=0$. The graphs intersect at two $x$-values.
Common mistakes
- A repeated root is one solution, not two distinct points.
- A line and a parabola cannot intersect in more than two points.
How to recognize it
- A system includes one linear equation and one quadratic equation.
- The answer choices are numbers of solutions or parameter conditions.
Další doporučená lekce
Zkuste dále Absolute value as distance and solution counts jako blízké osvěžení.
Absolute value as distance and solution countsSouvisející lekce
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