Notes

This printable supports Common Core Mathematics Standards HSF-IF.C.7c, HSF-IF.C.7d, HSF-IF.C.8a

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Quadratic Roots (Grades 11-12)

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Quadratic Roots

1. 
A fish jumps in the water near the dock. If its jump can be described in feet by the equation [math]y=-x^2+11x-30[/math], how far did the fish jump (the distance from exiting to re-entering the water)?
  1. 5 ft
  2. 6 ft
  3. 1.5 ft
  4. 1 ft
2. 
A belted kingfisher sits on a branch watching for fish in the water. When it sights a fish it dives from the branch and its flight path is described as [math]y=x^2-4.25x+4.125[/math] where y is the height and x is the time in seconds. At what times does the bird enter and exit the water?
  1. 1.5 s and 2.75 s
  2. -2.5 s and 1.75 s
  3. -1.5 s and -2.75 s
  4. 0 s and 4.125 s
3. 
A bridge with a parabolic arch crosses a highway that is 30 m wide. The arch is 6 m high in the center and 4 m high at the edges of the highway. How wide is the arch at ground level, to the nearest meter?
  1. 40 m
  2. 17 m
  3. 52 m
  4. 36 m
4. 
What are the roots of the equation [math]y=3x^2-16x+2[/math]?
  1. 3 , 2
  2. .2 , 5
  3. -.12 , -5.2
  4. .128 , 5.205
5. 
Determine the roots of the equation [math]y=-x^2-8x+2[/math].
  1. -8.24 , 0.24
  2. -6.02 , 2.04
  3. 8.42 , -2.04
  4. 6.02, -2.04
6. 
Determine the roots of the equation [math]y=6x^2+10x-24[/math].
  1. [math]-3[/math] , [math]-4[/math]
  2. [math]-3[/math] , [math]4/3[/math]
  3. [math]3[/math] , [math]3/4[/math]
  4. [math]3/4[/math] , [math]4/3[/math]
7. 
What are the roots of the equation [math]y=-x^2+120[/math]?
  1. [math]+-sqrt(120)[/math]
  2. [math]sqrt60[/math]
  3. [math]sqrt(120)[/math]
  4. [math]+-sqrt60[/math]
8. 
What are the roots of the equation [math]y=-4x^2+x-120[/math] ?
  1. 30 , -30
  2. 1 , -1
  3. 120 , -120
  4. No Real Roots
9. 
Determine the roots of the equation [math]y=-x^2+24x-143[/math].
  1. 2 , -143
  2. 11 , 13
  3. -11 , 13
  4. No Real Roots
10. 
A cyclist rides over a hill that can be described by the equation [math]y=-x^2+2x+24[/math], where [math]y[/math] is the height in meters and [math]x[/math] is the vertical distance in meters. How far is the start position from the end position in a straight line?
  1. 10 m
  2. 24 m
  3. 2 m
  4. 5 m

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