# Sample quiz on linear-quadratic systems Main home here.

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 $\cdots$?
$b=-\frac{21}{2}$
$b=-\frac{21}{4}$
$b=-\frac{4}{21}$
$b=\frac{21}{4}$