Sample quiz on vertex form parabola equation
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1. The quadratic with equation $y=4x^2$ passes through which of the points below?
   
   $(3,9)$
   $(2,8)$
   $(1,4)$
   $(1,16)$
   
2. If the quadratic $y=ax^2$ is to pass through the point $(1,8)$, determine the value of $a$.
   
   $a=8$
   $a=4$
   $a=\frac{1}{8}$
   $a=\frac{1}{4}$
3. Find the equation of a parabola with vertex at $(0,0)$ and passing through $(-2,20)$.
   
   $y=20x^2$
   $y=4x^2+4$
   $y=-5x^2$
   $y=5x^2$
4. Find the equation of a parabola with vertex at $(0,0)$ and passing through the point $(4,1)$.
   
   $y=16x^2$
   $y=\frac{1}{16}x^2$
   $y=\frac{1}{4}x^2$
   $y=4x^2$
5. Find the equation of a parabola with vertex at $(0,0)$ and passing through the point $(2,-1)$.
   
   $y=\frac{1}{4}x^2$
   $y=\frac{1}{2}x^2$
   $y=-\frac{1}{4}x^2$
   $y=-\frac{1}{2}x^2$
6. Which of the following quadratics passes through the point $(5,1)$?
   
   $y=x^2$
   $y=5x^2$
   $y=\frac{1}{5}x^2$
   $y=\frac{1}{25}x^2$
7. Find the equation of a parabola with vertex at $(1,-1)$ and going through the point $(0,0)$.
   
   $y=(x+1)^2-1$
   $y=(x-1)^2+1$
   $y=(x-1)^2-1$
   $y=(x+1)^2+1$
8. Find the equation of a parabola with vertex at $(-1,1)$ and going through the point $(-2,3)$
   
   $y=2(x-1)^2+1$
   $y=2(x+1)^2+1$
   $y=2(x+1)^2-1$
   $y=(x+2)^2+3$
9. Find the equation of a parabola with vertex at $(-3,-4)$ and going through the point $(-4,-3)$.
   
   $y=(x+3)^2-4$
   $y=(x+4)^2-3$
   $y=(x-3)^2+4$
   $y=(x+3)^2+4$
10. Find the equation of a parabola with vertex at $(5,6)$ and passing through the point $(6,5)$.
    
    $y=-(x-6)^2+5$
    $y=-(x-5)^2+6$
    $y=-(x-5)^2-6$
    $y=(x-6)^2+5$.
11. Which of the quadratics below has a $y$-intercept of $12$?
    
    $y=12x^2$
    $y=(x+3)^2-3$
    $y=(x+3)^2+3$
    $y=(x-3)^2+6$.
12. Which of the parabolas below has a $y$-intercept of $4$ and goes through $(1,3)$?
    
    $y=(x-1)^2+3$
    $y=(x+1)^2+3$
    $y=(x-1)^2-3$
    $y=(x-3)^2-5$.
13. Find the equation of a parabola with vertex at $(2,8)$ and $y$-intercept at $y=12$.
    
    $y=(x+2)^2+8$
    $y=(x-2)^2+8$
    $y=(x-2)^2-8$
    $y=(x-8)^2+2$.
14. Find the equation of a parabola with vertex at $(-3,6)$ and $y$-intercept at $y=0$.
    
    $y=-\frac{3}{2}(x+3)^2+6$
    $y=-\frac{2}{3}(x+3)^2+6$
    $y=-\frac{2}{3}(x-3)^2-6$
    $y=-\frac{3}{2}(x+3)^2-6$.
15. Find the equation of a parabola with vertex at $(2,10)$ and one $x$-intercept at $x=-2$.
    
    $y=-\frac{5}{8}(x+2)^2+10$
    $y=-\frac{8}{5}(x+2)^2-10$
    $y=-\frac{8}{5}(x-2)^2+10$
    $y=-\frac{5}{8}(x-2)^2+10$.
16. Find the equation of a parabola with vertex at $(-2,-2)$ and $y$-intercept at $y=0$.
    
    $y=\frac{1}{2}(x-2)^2+2$
    $y=\frac{1}{2}(x-2)^2-2$
    $y=\frac{1}{2}(x+2)^2-2$
    $y=2(x+2)^2-2$.
17. Find the equation of a parabola with vertex at $(-3,2)$ and one $x$-intercept at $x=3$.
    
    $y=-\frac{1}{18}(x-3)^2+2$
    $y=-\frac{1}{18}(x+3)^2+2$
    $y=-18(x+3)^2+2$
    $y=-18(x-3)^2+2$.
18. Find the equation of a parabola with vertex at $(5,5)$ and passing through the point $(6,6)$.
    
    $y=(x-5)^2+5$
    $y=(x+5)^2+5$
    $y=(x-6)^2+6$
    $y=(x-6)^2+5$.
19. Find the equation of a parabola with vertex at $(-4,6)$ and one $x$-intercept at $x=-4$.
    
    $y=(x-4)^2+6$
    $y=(x+4)^2+6$
    $y=(x+4)^2-6$
    Impossible.
20. Find the equation of a parabola with vertex at $(h,k)$ and passing through the point $(k,h)$, for $h\neq k$.
    
    $y=\frac{1}{k-h}(x-h)^2+k$
    $y=\frac{1}{h-k}(x-h)^2+k$
    $y=\frac{1}{h-k}(x+h)^2+k$
    $y=\frac{1}{k-h}(x-h)^2-k$.