Sample quiz on linear-quadratic systems
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- If a line and a parabola intersect at just one point, the line is called $\cdots$?
- If a line intersects a parabola at two distinct points, the line is called $\cdots$?
- Regarding the intersection of $y=mx+k$ and $y=ax^2+bx+c$, how many possibilities are there?
- A condition for the line $y=mx+b~(b\neq 0)$ to be a tangent to the parent parabola $y=x^2$ is $\cdots$?
- Solve the linear-quadratic system $y=x,~y=x^2$.
- How many points of intersection are there between $y=-x-1$ and $y=x^2$?
- Solve the linear-quadratic system $3x+2y+3=0,~x^2-3y=0$.
- Solve the linear-quadratic system $y=x+1,~y=x^2-2x+3$
- Solve the linear-quadratic system $y=2x-1,~y=3x^2-4x+2$
- The line $y=2x+b$ is to intersect the quadratic $y=x^2-3x+1$ just once. The value of $b$ must be $\cdots$?