Critical Points of a Parabola
Identify the y-int in the equation
y=x2 + 3x +10
(0,10)
(2x2 + 3x - 7) + (3x2 -4x -10)
5x2 - x -17
At a festival, pumpkins are launched with large catapults and air cannons. On one launch, the height of a pumpkin in feet above the ground after t seconds is modeled by h=20+90t-16t2
From what height was the pumpkin launched?
20 feet
x^2 - 16 = 0
(x+4) ( x-4)
x2 - 16 = 0
x= -4, x = 4
Identify the amplitude in the equation
y = 3x2 - 12x +10
a = 3
(5x2 - 12x +1) - (2x2 +3x - 7)
3x2 -15x +8
The length of a rectangle is 7 more than the width. If the area of the rectangle is 60 square inches, what are the dimensions of the rectangle?
5 X 12
X^2 + 7x +10 = 0
(x+5 (x+2)
x2 +7x +10 = 0
x = -5 , x = -2
Identify the vertex of the equation
y = 3x2 - 12x +10
(2,-10)
(3x-5)(x-8)
3x2 - 29x +40
At a festival, pumpkins are launched with large catapults and air cannons. On one launch, the height of a pumpkin in feet above the ground after t seconds is modeled by h=20+90t-16t2
How long was the pumpkin in the air? Round your answer to the nearest hundredth
5.84 seconds
2x2 - 7x -15 = 0
(2x+3) (x-5)
2x2 - 7x - 15 = 0
x = -3/2 , x = 5
y = x2 +3x + 10
(-2,0) and (5,0)
(2x - 4)(x+3)
2x2 + 2x - 12
A flare is lunched up with an initial velocity of 64 feet per second from the top of a 200 foot building. The equation h(t)=-16t2+64t+200 models this situation. Determine the maximum height of the flare and the time it takes to reach that maximum.
264 feet in 2 seconds
10x2 +17x + 3
(2x+3) (5x+1)
9x2 - 9x +2 = 0
x = 1/3 , x = 2/3
Identify the x-int of the equation
y = 2x2 - 12x +10
(5,0) and (1,0)
(3x - 4)(3x - 1)
9x2 - 15x +4
At a swim meet, Janet dives from a diving board that is 20 feet high. Her position above the ware is represented by the equation y=-16x2+24x+20, where x represents the time in seconds and y represents the height above the water. After how many seconds does Janet enter the water?
2.096 seconds
3x2 +17x +10
(x+5) (3x+2)
2x2 + 5x - 3 = 0
x = -3 , x = 1/2