Quadratic applications
A ball is thrown upward from a height of 4 feet with an initial velocity of 32 ft/s. The height of the ball after t seconds is given by:h(t)=−16t^2+32t+4
After how many seconds does the ball hit the ground?
Solve the equation by taking the square root :
x2=9
x = plus or minus 3
Factor the polynomial using the difference of two squares :
x2-4
(x-2)(x+2)
Solve by using the Quadratic Formula
3x2+9x-2=0
-9 plus or minus square root 105 divided by 6
Solve the Quadratics by Factoring
x2-12x+20=0
10, 2
A basketball is shot, and its height (in feet) after t seconds is modeled by: h(t)=−16t^2+40t+6
What is the maximum height the basketball reaches?
31 feet
Solve the equation by taking the square root :
7x2=63
x = plus or minus 3
Factor the polynomial using the difference of two squares :
81x2-25
(9x+5)(9x-5)
Solve by using the Quadratic Formula
2x2-5=9x
x = 5 , -1/2
Solve the Quadratics by Factoring
x2+6x+4=-4
-2, -4
A rectangular garden has a length that is 6 feet longer than its width. The perimeter of the garden is 84 feet.
What are the dimensions of the rectangle?
18 ft by 24 ft
Solve the equation by taking the square root :
x2+9=13
x = plus or minus 2
Factor the polynomial using the difference of two squares :
x2+16
PRIME
Solve by using the Quadratic Formula
6x2-12x=-6
x = 1
Solve the Quadratics by Factoring
n2-18n-5=-50
3, 15
A diver jumps off a board 10 feet above the water. The height is modeled by: h(t)=−16t^2+24t+10
How far above the water is the diver at 1.5 seconds?
10 feet
Solve the equation by taking the square root :
7x2-3=459
x = plus or minus 8.1
Factor the polynomial using the difference of two squares :
50x2-32
2(5x+4)(5x-4)
Solve by using the Quadratic Formula
2x2+2x=5
x = -2.16 or 1.16
Solve the Quadratics by Factoring
x2+12x-20=8
2 and -14
A soccer ball is kicked, and its height (in feet) is modeled by: h(t)=−16t^2+48t+1
When is the ball at a height of 33 feet?
1 and 2 seconds
Solve the equation by taking the square root :
6x2-9=255
x = plus or minus 6.6
Factor the polynomial using the difference of two squares :
36x3-100x
4x(3x+5)(3x-5)
Solve by using the Quadratic Formula
2x2+9=-11x
x = -1, -9/2
Solve the Quadratics by Factoring
x2-8x+8=17
-1, 9