Factoring
x2 + 3 x - 10
(x - 2) (x + 5)
x2-3x-10 =y
Find the roots from this equation
(5,0) (-2,0)
The pathway of a frog jumping onto a lily pad can be represented by the equation
h = -0.5t2 + 3t + 2
(where t = time in seconds and h = height in feet)
What is the maximum height of the frog?
6.5 FT
Marsha threw her math book off a 30-foot building. The equation of the book can be represented by the equation:
h= -16t2 + 24t + 30
What is the maximum height of Marsha's math book?
39 ft
t= -24/2(-16) = 0.75
h= -16(0.75)2+24(0.75) +30
x2 - 9 x + 18
(x - 3) (x - 6)
Solve for x: x2-18x+45 = 0
(Solve for x when y is equal to zero which is get the roots of this equation)
x = 15 or x = 3
After t seconds, a ball tossed in the air from the ground level reaches a height of h feet given by the function h(t) = 144t – 16t2.
a. What is the height of the ball after 3 seconds?
b. What is the maximum height the ball will reach?
a. 288 ft
b. 324 ft
To practice catching, the little league team uses a baseball throwing machine. The pathway of the ball from the machine can be represented by the equation
h= -16t2 + 48t +4
What will be the height of the ball after 2 seconds?
(Keep in mind t= time in seconds and h= height in feet)
36 ft
3 x2 + 5 x + 2
(3 x + 2) (x + 1)
Find the vertex and the y-intercept. In addition, find the x-intercepts if they exist.
y=−x2−2x+15
vertex: (-1,16)
y intercept: (0,15)
roots/ x-intercepts: (-5,0)(3,0)
A rocket carrying fireworks is launched from a hill 80 feet above a lake. The rocket will fall into the lake after exploding at its maximum height. The rocket’s height above the surface of the lake is given by the function
h(t) = -16t2 + 64t + 80.
a. What is the height of the rocket after 1.5 seconds?
b. What is the maximum height reached by the rocket?
a. 140 ft
b. 144 ft
While working on a roof Rob dropped his hammer. The hammer's fall can be represented by the equation:
h = -16t2 + 20
How long will it take the hammer to reach the ground?
1.12 s
2x2 + 10x + 12
2(x + 2)(x + 3)
Find the vertex, the x intecrepts and the y intercept.
y= x2 + 8x +15
Y-intercept= (0,15)
Roots: (-3,0)(-5,0)
Vertex:(-4,-1)
Sean tossed a coin off the bridge into the stream below. The path of the coin can be represented by the equation:
h = -16t +72t +100
How long will it take the coin to reach the stream?
5.61 s
The path of a toy rocket fired into the air can be represented by the equation
h = -16t2 + 75t
What is the height of the rocket after 3 seconds?
(t is time and h is height)
81 ft