Graph Characteristics
What do we call the graph of the function y=ax2+bx+c?
Parabola
Simplify: 3x2+2x2
5x2
Simplify: x(3x-1)
3x2-x
Factor: 5x2+10x
5x(x+2)
A bird dives towards the water. The height, h, in meters, of the bird above the water t seconds after it begins its dive can be approximated by the function h(t)=5t2-30t+45.
What is the starting height of the bird?
45 meters
What is the y-intercept of the graph y=x2+4x-1?
(0, -1)
Simplify: (2x2+4x)+(-x2+3x)
x2+7x
Simplify: (x+1)(x+2)
x2+3x+2
Solve: 14x2-7x=0
7x(2x-1)=0
{0, 1/2}
A bird dives towards the water. The height, h, in meters, of the bird above the water t seconds after it begins its dive can be approximated by the function h(t)=5t2-30t+45.
When does it hit the water?
3 seconds
Which way does the graph of y=-3x2+4x-1 open?
Down
Simplify: (x2+3x-4)+(3x2-10x+12)
4x2-7x+8
Simplify: (3x+1)(x-2)
3x2-5x-2
Factor: x2-7x+10
(x-5)(x-2)
A flare is launched from a boat. The height h, in meters, of the flare above the water is approximately modeled by the function h(t)=-15t2+150t, where t is the number of seconds after the flare is launched.
How many seconds will it take for the flare to return to the water?
10 seconds
How many x-intercepts does y=x2+1 have?
None
Simplify: (-3x2+10x)-(x2+5x+1)
-4x25x-1
Simplify: (x-4)(x+4)
x2-16
Solve: 2x2+16x+24=0
2(x+6)(x+2)=0
{-6, -2}
Ted popped a baseball straight up with an initial upwards velocity of 48 ft/s. The height h, in feet, of the ball above the ground is modeled by the function h(t)=-16t2+48t+3.
How long was the ball in the air if the catcher catches the ball 3 feet above the ground?
3 seconds
What are the x-intercepts of y=(x-1)(x+2)?
{1, -2}
Simplify: (4x2+8x-10)-(-x2-2x-10)
5x2+10x
Simplify: (x+2)2
x2+4x+4
(2x+3)(x+1)=0
{-1, -3/2}
A company models its net profit, in thousands of dollars, with the function f(x)=9x2-54x-144, where x is the number of units of its product sold.
How many units does the company need to sell to break even?
8 units