Sample quiz on linear-quadratic systems
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1. If a line and a parabola intersect at just one point, the line is called $\cdots$?
   
   a hyperbola
   a secant
   a tangent
   a diameter
   
2. If a line intersects a parabola at two distinct points, the line is called $\cdots$?
   
   a secant
   a tangent
   a diameter
   a directrix
3. Regarding the intersection of $y=mx+k$ and $y=ax^2+bx+c$, how many possibilities are there?
   
   $0$
   $1$
   $2$
   $3$
4. A condition for the line $y=mx+b~(b\neq 0)$ to be a tangent to the parent parabola $y=x^2$ is $\cdots$?
   
   $b^2+4m=0$
   $b+4m=0$
   $m+4b=0$
   $m^2+4b=0$
5. Solve the linear-quadratic system $y=x,~y=x^2$.
   
   $\{(0,0)\}$
   $\{(1,1)\}$
   $\{(0,0),(1,1)\}$
   $\{(0,0),(-1,1)\}$.
6. How many points of intersection are there between $y=-x-1$ and $y=x^2$?
   
   $0$
   $1$
   $2$
   $3$
7. Solve the linear-quadratic system $3x+2y+3=0,~x^2-3y=0$.
   
   $\{(-3,3),(-\frac{3}{2},\frac{3}{4})\}$
   $\{(-3,3),(\frac{3}{4},\frac{3}{2})\}$
   $\{(3,-3),(\frac{3}{4},-\frac{3}{2})\}$
   $\{(3,-3),(-\frac{2}{3},\frac{3}{4})\}$
8. Solve the linear-quadratic system $y=x+1,~y=x^2-2x+3$
   
   $\{(1,2),(3,2)\}$
   $\{(0,1),(2,3)\}$
   $\{(1,2),(2,3)\}$
   $\{(-1,0),(1,2)\}$
9. Solve the linear-quadratic system $y=2x-1,~y=3x^2-4x+2$
   
   $\{(0,-1),(1,1)\}$
   $\{(-1,-3),(2,6)\}$
   $\{(-1,-3),(-2,-5)\}$
   $\{(1,1)\}$
10. The line $y=2x+b$ is to intersect the quadratic $y=x^2-3x+1$ just once. The value of $b$ must be $\cdots$?
    
    $b=-\frac{21}{2}$
    $b=-\frac{21}{4}$
    $b=-\frac{4}{21}$
    $b=\frac{21}{4}$