Property 6
Conditions of Parabola in Relation to a Line
For \(y=ax^2+bx+c\) and \(y=mx+n\), joint solutions give
\(ax^2+(b-m)x+c-n=0\)
The discriminant is analysed.
\(\Delta>0\): line cuts the parabola in two points.
\(\Delta=0\): line is tangent to the parabola.
\(\Delta<0\): line does not cut the parabola.
1.
\(f(x)=x^2-4x\)
\(g(x)=x-4\)
\(A=?\)
2.
\(f(x)=x^2\)
\(g(x)=2-x\)
\(A=?\)
3.
\(f(x)=x^2+3x+7\)
\(g(x)=x+6\)
\(A=?\)
4.
\(f(x)=x^2-5x+8\)
\(g(x)=k-x\)
\(k=?\)
5.
\(f(x)=x^2+7x+10\)
\(g(x)=x+k\)
\(k=?\)
6.
\(f(x)=x^2-x+5\)
\(g(x)=x+k\)
\(A=?\)
7.
\(A=?\)
8.
\(g(x)=2x^2-x\)
\(f(x)=x^2\)
\(|OA|=?\)
9.
\(y=x^2-1\)
\(y=-x^2+7\)
\(|AB|=?\)
10.
\(f(x)=x^2+x+1\)
\(g(x)=2x+3\)
\(|AB|=?\)