# 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)?

- 5 ft
- 6 ft
- 1.5 ft
- 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?

- 1.5 s and 2.75 s
- -2.5 s and 1.75 s
- -1.5 s and -2.75 s
- 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?

- 40 m
- 17 m
- 52 m
- 36 m

4.

What are the roots of the equation [math]y=3x^2-16x+2[/math]?

- 3 , 2
- .2 , 5
- -.12 , -5.2
- .128 , 5.205

5.

Determine the roots of the equation [math]y=-x^2-8x+2[/math].

- -8.24 , 0.24
- -6.02 , 2.04
- 8.42 , -2.04
- 6.02, -2.04

6.

Determine the roots of the equation [math]y=6x^2+10x-24[/math].

- [math]-3[/math] , [math]-4[/math]
- [math]-3[/math] , [math]4/3[/math]
- [math]3[/math] , [math]3/4[/math]
- [math]3/4[/math] , [math]4/3[/math]

7.

What are the roots of the equation [math]y=-x^2+120[/math]?

- [math]+-sqrt(120)[/math]
- [math]sqrt60[/math]
- [math]sqrt(120)[/math]
- [math]+-sqrt60[/math]

8.

What are the roots of the equation [math]y=-4x^2+x-120[/math] ?

- 30 , -30
- 1 , -1
- 120 , -120
- No Real Roots

9.

Determine the roots of the equation [math]y=-x^2+24x-143[/math].

- 2 , -143
- 11 , 13
- -11 , 13
- 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?

- 10 m
- 24 m
- 2 m
- 5 m

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