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Property 6

Conditions of Parabola in Relation to a Line

\(y=ax^2+bx+c\)
\(y=mx+n\)

(Joint solutions are made)

\(ax^2+bx+c=mx+n\)
\(ax^2+(b-m)x+c-n=0\)

(Discrement of Δ is analyzed)

  • \(\Delta>0\)

    Line cuts the equation in two points.

  • \(\Delta=0\)

    Line is tangent to parabola.

  • \(\Delta<0\)

    Line does not cut the parabola.

1.
\(\Rightarrow A=?\)
2.
\(\Rightarrow A=?\)
3.
\(\Rightarrow A=?\)
4.
\(\Rightarrow k=?\)