Sample quiz on word problems involving quadratics
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1. The hypotenuse of a right triangle measures $(2x+1)$ units, while the legs are $2x$ and $(x-1)$ units. Find the value of $x$.
   
   A: $0$
   B: $5$
   C: $6$
   D: $8$
   
2. Assuming $x> 0$, find the value of $x$ for which $(x,x+1,x+2)$ is a pythagorean triple.
   
   A: $3$
   B: $4$
   C: $2$
   D: $-1$
3. At any time $t$, the height $h$ of an object thrown up is given by $h=-4.9t^2+14.7t$. Find the initial height of the object.
   
   A: $14.7$
   B: $4.9$
   C: $9.8$
   D: $0$
4. At any time $t$, the height $h$ of an object thrown up is given by $h=-5t^2+20t$. At what time does it attain its maximum height?
   
   A: $t=20$
   B: $t=4$
   C: $t=3$
   D: $t=2$
5. At any time $t$ seconds, the height $h$ of an object thrown up is given by $h=-4.9t^2+19.6t+3$ (in meters). Which statement is wrong?
   
   A: It attained its maximum at $t=2$ s
   B: Its initial height is $3$ m
   C: Its maximum height is $22.6$ m
   D: It spent at total of $49$ s in the air.
6. The profit function for a certain item is given by $P(x)=-5x^2+300x$, where $x$ is the number of items. What is the break-even point?
   
   A: $x=30$
   B: $x=40$
   C: $x=0$ or $x=60$
   D: $x=0$ or $x=30$
7. The length and width of a rectangle are $(x+3)$ and $(x-2)$. Find $x$ if its area is $50$ sq. units.
   
   A: $7$
   B: $8$
   C: $-7$
   D: $-8$
8. A square measures $(2x-1)\times(2x-1)$. Its area is $49$ sq. units. Find the admissible value of $x$.
   
   A: $x=8$
   B: $x=7$
   C: $x=4$
   D: $x=-3$
9. Find the distance between the points of intersection of the quadratics $y=x^2$ and $y=-x^2+6x+8$.
   
   A: $5\sqrt{10}$
   B: $5\sqrt{3}$
   C: $10\sqrt{5}$
   D: $5$
10. Find two consecutive positive numbers numbers whose squares add up to $85$.
    
    A: $5,6$
    B: $6,8$
    C: $7,8$
    D: $6,7$