Graphs
Does this parabola open up or down?
y=-3x+7-7x^2
Down
Factor completely:
-14x^2+2x
-2x(7x-1)
Solve for the roots:
x^2-144=0
x=+-12
The stone's height (in meters above the water), x seconds after Alan threw it, is modeled by:
h(x)=-5x^2+10x+15
What is the height of the stone at the time it is thrown?
15 meters
Does this parabola have a minimum or a maximum?
y=3x^2-2x+1
Minimum
Factor completely:
12x^2-27
3(2x+3)(2x-3)
Solve for the zeros:
x^2-13x+30=0
x=10 and x=3
Aaron throws a ball off of the roof of a building. The path of the ball is given by the function:
h(t)=-16t^2+20t+50
What is the height (in feet) of the ball after 1.5 seconds?
44 feet
What is the vertex and y-intercept of
f(x)=-2(x+3)^2-1
Vertex:
(-3,-1)
Y-intercept:
(0,-19)
Factor completely:
6x^2-5x+1
(3x-1)(2x-1)
Solve for the x-intercepts:
18x^2-50=0
x=+-5/3
Rui is a professional deep water free diver. His altitude (in meters relative to sea level), x seconds after diving, is modeled by:
h(t)=0.5t^2-10t
What is the lowest (minimum) altitude Rui will reach? How long will it take for Rui to get there?
10 seconds to reach 50 meters below sea level.
What is the vertex of
2x^2-12x+1
(3,-17)
Factor completely:
6x^2-28x-160
2(3x+10)(x-8)
What are the solutions for:
2x^2-9x=5
x=-0.5 and x=5
An object is launched from a platform.
Its height (in meters), x seconds after the launch, is modeled by:
h(x)=-5x^2+20x+60
How many seconds after launch will the object land on the ground?
6 seconds