Sample quiz on factors and $x$-intercepts Main home here.

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 $y=-2(3x-5)(6x+7)$.
$70$
$35$
$-35$
$-70$.