Sample quiz on key features of a parabola
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1. Which of the following is true for quadratic relations?
   
   the first differences are equal
   the second differences are equal
   the third differences are equal
   the fourth differences are equal
   
2. Which of the following is a quadratic relation?
   
   $y=x^2$
   $y=2^{x}$
   $y=2x$
   $y=x^3$
3. Which of the following is not a quadratic relation?
   
   $y=2(x+1)(x-3)$
   $y=2(x-2)^2(x+1)$
   $y=2(x-3)^2-8$
   $y=2x^2+8x-10$
4. What is the value of the constant second differences for the quadratic relation $y=x^2$?
   
   $1$
   $2$
   $-1$
   $-2$
5. What is the value of the constant second differences for the quadratic relation $y=-x^2$?
   
   $1$
   $2$
   $-2$
   $-1$
6. What is the value of the constant second differences for the quadratic relation $y=\frac{1}{2}x^2$?
   
   $1$
   $2$
   $-1$
   $-2$
7. What is the value of the constant second differences for the quadratic relation $y=3x^2$?
   
   $2$
   $3$
   $4$
   $6$
8. What is the equation of the axis of symmetry for the quadratic relation $y=-2(x-2)^2-1$?
   
   $x=-2$
   $x=-1$
   $x=1$
   $x=2$
9. What is the equation of the axis of symmetry for the quadratic relation $y=2(x+2)^2+1$?
   
   $y=-2$
   $x=-2$
   $y=2$
   $x=2$
10. Find the vertex of the parabola $y=(x+2)^2-3$
    
    $(-3,-2)$
    $(-2,-3)$
    $(-2,3)$
    $(2,-3)$
11. Find the vertex of the parabola $y=(x-2)^2-3$
    
    $(-3,-2)$
    $(-2,-3)$
    $(-2,3)$
    $(2,-3)$
12. Which of the following statements is true concerning the parabola $y=2(x-2)^2-8$?
    
    it has a minimum value of $8$
    it has a maximum value of $-8$
    it has a minimum value of $-8$
    it has a maximum value of $8$
13. Which statement is true concerning the parabola $y=-3(x-2)^2-12$?
    
    it has a maximum value of $-12$
    it has a minimum value of $-12$
    it has a maximum value of $12$
    it has a minimum value of $12$
14. What is the equation of the axis of symmetry for the parabola $y=x^2-4x+4$?
    
    $y=4$
    $x=4$
    $y=2$
    $x=2$
15. What is the $y$-intercept of the quadratic $y=x^2+4x+1$?
    
    $y=1$
    $y=4$
    $y=0$
    $y=-1$
16. Find the zeros of the quadratic $y=5(x-2)(x+3)$
    
    $x=5, 2$
    $x=5, -3$
    $x=3,-2$
    $x=2,-3$
17. Find the zeros of the quadratic $y=-5(x+1)(x-3)$
    
    $x=-5, -1$
    $x=-5, 3$
    $x=-1, 3$
    $x=-1, -3$
18. Find the $y$-intercept of the quadratic $y=5(x-2)(x+3)$
    
    $y=-10$
    $y=-30$
    $y=-6$
    $y=30$
19. Find the minimum value of the quadratic $y=-2(x+3)^2-18$
    
    $-18$
    $-2$
    $18$
    it has no minimum value
20. Find the maximum value of the quadratic $y=5(x-2)^2+45$
    
    it has no maximum value
    $45$
    $5$
    $0$