Graphing
Solve the equation by graphing: x2-4x=0
(Must show graph for full credit)
Solutions: (0,0) and (4,0)
Solve using square roots: x2-16=0.
Solutions: (4,0) and (-4,0)
Find the value of c that completes the square: x2+12x+c
c=36
Solve using the quadratic formula. Round to the nearest tenth if necessary: x2-12x+36=0
(6,0)
Solve the following system by graphing:
y=x2-2x+1
y=x+1
(0,1) and (3,4)
Solve the equation by graphing: x2-2x+5=0
(Must show graph for full credit)
Solution: No solution
Solve using square roots: -3x2+8=8
Solution (0,0)
Solve by completing the square: x2+2x=3
Solutions (-3,0) and (1,0)
Solve using the quadratic formula. Round to the nearest tenth if necessary: 2x2-6x+5=0
No real solutions
Solve the following system by substitution:
y=2x2+3x-4
y-4x=2
(-3/2,-4) and (2,10)
Solve the equation by graphing: 3x-18=-x2.
(Must show graph for full credit)
Solutions: (-6,0) and (3,0)
A box falls off a warehouse shelf from a height of 16 feet. The function h = -16t2+16 gives the height h (in feet) of the box after x seconds. When does it hit the floor? (Solve using square roots)
After 1 second.
Solve by completing the square: x2+5x-7=-14
No real solutions
Solve using the quadratic formula. Round to the nearest tenth if necessary: 5x2-2=4x
(-0.3,0) and (1.1, 0)
Solve the following system by elimination:
y=-2x
y=x2+3x
(0,0) and (-5,10)
The height y (in yards) of a flop shot in gold can be modeled by y=-x2+5x, where x is the horizontal distance (in yards).
How far away does the golf ball land? (Solve by graphing)
5 yards
Solve using square roots: 9(x+1)2=16
Solutions: (-7/3,0) and (1/3,0)
Find the value(s) of b that makes x2+bx+25 a perfect square trinomial.
b= 10 and -10
A swimmer takes a running jump off a pier. The path of the swimmer can be modeled by the equation h= -0.1d2+0.1d+3 , where h is the height (in feet) and d is the horizontal distance (in feet). How far from the pier does the swimmer enter the water?
6 feet
Solve the following system by elimination:
y=-2x2+x-3
y=2x-2
No real solution
A baseball player throws a baseball with an upward velocity of 24 feet per second. The release point is 6 feet above the ground. The function h=-16t2+24t+6 gives the height h (in feet) of the baseball after t seconds.
How long does the ball remain above 6 feet?
(Solve by graphing)
1.5 seconds
A rectangle has the side lengths of 2x and 3x. Its total area is 78 cm2.
What are the exact side lengths of the rectangle in cm?
(Do not round, exact answers only)
3sqrt13 and 2sqrt13
The area of a patio is 216 ft2.
In the dimensions of the blue print, the side lengths are x and (x+6).
What are the exact measurements of the side lengths?
12ft by 18ft
The distance d (in feet) it takes to stop a car traveling v miles per hour can be modeled by d=0.05v2+2.2v . It takes a car 235 feet to stop. How fast was the car going when the brakes were applied?
50 miles per hour
The attendance y for two movies can be modeled by the following equations, where x is the number of days since the movies opened.
y=-x2+35x+100 (Movie A)
y=-5x+275 (Movie B)
When is the attendance for each movie the same?
After 5 days and 35 days.