Graphs
Does this parabola open up or down?
y=-3x+7-7x^2
Down
Factor completely:
x^2-169
(x-13)(x+13)
Solve for the x-intercepts:
2x(3x+1)=0
x=0,-1/3
Which part of standard form would tell you how high off the ground something starts at?
the constant (c)
What is the fraction equivalent of .03125 ?
1/32
Does this parabola have a minimum or a maximum?
y=3x^2-2x+1
Minimum
Factor completely:
-14x^2+2x
-2x(7x-1)
Solve for the roots:
x^2=144
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
Evaluate
f(-2)
for
f(x)=2x^2-5x-9
f(-2)=9
Give an example of a parabola in standard form that has a y-intercept of (0,30).
Any parabola whose c=30
Factor completely:
6x^2-5x+1
(3x-1)(2x-1)
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
Convert to standard form:
(3x+1)(5x-6)
15x^2-13x-6
What is the vertex of
2x^2-12x+1
(3,-17)
Factor completely:
12x^2-27
3(2x+3)(2x-3)
What are the solutions for:
2x^2-9x=5
x=-0.5 and x=5
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.
Using the discriminant, how many solutions does
25x^2+80x+64
1 solution
Give an example of a parabola in standard form whose x-intercepts are
x=-2 and x=7
EX:
x^2-5x-14
Factor completely:
6x^2-28x-160
2(3x+10)(x-8)
Solve for the roots:
x^2+18x+4=0
x=-17.78 and x=-0.23
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
{(2x,+,y,=,6),(x,-,y,=,-3):}
(1,4)