Sample quiz on factors and $x$-intercepts
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1. The $x$-intercepts of a quadratic are the points where $\cdots$
   
   $x=0$
   $y=0$
   $x=0$ or $y=0$
   $x=0$ and $y=0$
   
2. What is the maximum number of $x$-intercepts a quadratic can have?
   
   $3$
   $2$
   $1$
   $0$
3. What is the minimum number of $x$-intercepts a quadratic can have?
   
   $3$
   $2$
   $1$
   $0$
4. An $x$-intercept can also be referred to as a solution, a zero, or a $\cdots$
   
   root
   vertex
   minimum
   maximum
5. Find the $x$-intercepts of the quadratic $y=(x-1)(x+2)$
   
   $x=1,2$
   $x=2,-1$
   $x=1,-2$
   $x=-1,-2$.
6. Find the $x$-intercepts of the quadratic $y=(2x+1)(x-2)$
   
   $x=2,-\frac{1}{2}$
   $x=2,\frac{1}{2}$
   $x=-2,\frac{1}{2}$
   $x=-2,-\frac{1}{2}$
7. Find the $x$-intercepts of the quadratic $y=(3x+1)(2x+5)$.
   
   $x=-1,-5$
   $x=\frac{1}{3},\frac{5}{2}$
   $x=-\frac{1}{3},-\frac{5}{2}$
   $x=-\frac{1}{3},-\frac{2}{5}$
8. Find the $x$-intercepts of the quadratic $y=x^2+x-2$
   
   $x=-1,2$
   $x=-2,1$
   $x=-2,-1$
   $x=2,1$
9. Find the $x$-intercepts of the quadratic $y=3x^2+10x+3$
   
   $x=-3,-\frac{1}{3}$
   $x=-3,-\frac{10}{3}$
   $x=-3,\frac{10}{3}$
   $x=3,\frac{1}{3}$
10. Find the $x$-intercept(s) of the quadratic $y=x^2+4x+4$.
    
    $x=-4$
    $x=-2$
    $x=-2,2$
    $x=-4,4$.
11. What is the equation of the axis of symmetry of the quadratic $y=(x-1)(x+3)$?
    
    $x=1$
    $x=-2$
    $x=-3$
    $x=-1$.
12. Find the equation of the axis of symmetry for the quadratic $y=(2x+1)(2x-1)$.
    
    $y=0$
    $x=0$
    $x=-\frac{1}{2}$
    $x=-\frac{1}{4}$.
13. Find the coordinates of the vertex of the quadratic $y=2(x-3)(x+3)$.
    
    $(0,-9)$
    $(0,-18)$
    $(0,-6)$
    $(0,18)$.
14. Find the equation of a quadratic with $x$-intercepts $x=1,-3$ and passing through $(2,10)$.
    
    $y=(x-1)(x+3)$
    $y=2(x-1)(x-3)$
    $y=5(x-1)(x+3)$
    $y=2(x-1)(x+3)$.
15. Find the equation of a quadratic with $x$-intercepts $x=\frac{2}{5},-\frac{1}{3}$ passing through $(0,4)$.
    
    $y=-2(5x+2)(3x+1)($
    $y=-2(5x-2)(3x+1)$
    $y=-2(5x-2)(3x-1)$
    $y=-2(5x+4)(3x-1)$.
16. Find the minimum value of the quadratic $y=(x+2)(x-6)$.
    
    $-16$
    $-8$
    $-4$
    $0$.
17. Find the maximum value of the quadratic $y=(x-3)(x+5)$.
    
    $16$
    $-16$
    $-15$
    None.
18. At what value of $x$ does the quadratic $y=(2x-1)(3x+5)$ attain its minimum value?
    
    $x=-\frac{7}{6}$
    $x=-\frac{5}{3}$
    $x=-\frac{7}{12}$
    $x=\frac{7}{12}$.
19. For what value of $c$ does the quadratic $y=x^2-6x+c$ have an $x$-intercept of $x=7$?
    
    $c=-6$
    $c=-7$
    $c=7$
    $c=6$.
20. Find the maximum value of the quadratic $y=-2(3x-5)(6x+7)$.
    
    $70$
    $35$
    $-35$
    $-70$.