Solve Quadratic Systems (HSC SSCE Mathematics Advanced): Flashcards

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Solve Quadratic Systems
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Quadratic system definition

Finding where two functions intersect

Intersection points meaning

Points where two graphs cross or meet

First step in algebraic method

Set the two functions equal: f(x)=g(x)f(x) = g(x)

Discriminant formula

Δ=b24ac\Delta = b^2 - 4ac

Intersections when Δ>0\Delta > 0

Two intersection points

Intersections when Δ=0\Delta = 0

One intersection point (tangent)

Intersections when Δ<0\Delta < 0

No intersection points

Graphical method steps

Plot both, identify where they intersect

Best method for two quadratics

Quadratic formula (most reliable)

Using linear eq. for y-values

Quicker than quadratic equation

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