Polynomials
(-4x2+2x-3)+(5x2-4x+8)
x2-2x+5
Factor 14n2+10n
2n(7n+5)
Simplify sqrt(75)
5 * sqrt(3)
Find the axis of symmetry for the equation y = 2x2+8x-5.
x = -2
Calculator active: A ball being thrown in the air can be modeled by the equation h=-4.9t2+14t+49, where h represents height in feet and t represents time in seconds. How long does it take for the ball to reach its maximum height?
1.43 seconds
(6x2+4)-(3x2+5)
3x2-1
Factor m3-m2+2m-2
(m2+2)(m-1)
Simplify sqrt(512m3)
16m*sqrt(2m)
Find the vertex of y = -3x2+18x-13 without a graph.
(3, 14)
Calculator active: The equation -15t2+60t+3 represents the height of a water balloon at t seconds. How long will it take for the water balloon to hit the ground?
3.95 seconds
(2x-5)(3x+2)
6x2-4x-10
Factor m2-11m+18
(m-9)(m-2)
Simplify sqrt(18) + sqrt(2)
4 * sqrt(2)
Find the zeros by factoring: x2+4x=0
x = -4 and x = 0
Calculator active: -16t2+64t+80 represents the height of a rocket at t time in seconds. How long does it take the rocket to reach 100 ft on its ascent?
0.34 seconds
(2x-4)(3x2-6x+1)
6x3-24x2+26x-4
Factor 3x2+7x+4
(3x+4)(x+1)
Find the area of a rectangle with length = sqrt(24) and width = sqrt(8)
8*sqrt(3)
Solve the following quadratic equation by using the quadratic formula: y = 4x2-17x-15
x = 5 and x = -3/4
The equation P=-3x2+12x+2 represents the amount of P profit for the x cost of an item. What is the maximum profit for the sale of the item?
$14
(2x2-4x+6)(x2+5x-2)
2x4+6x3-18x2+38x-12
Factor 30t3+50t2-20t
If P is power (in watts) and R is resistance (in ohms), then the voltage V necessary to run the circuit is V = sqrt(PR). Find the voltage necessary to run a 40-watt amplifier with a resistance of 150 ohms.
20*sqrt(15)
Solve the following quadratic equation by completing the square: x2+10x+16=0. MUST SHOW WORK!
x = -2 and x = -8
The equation h=-16t2+198t+25 represents the height of a diver jumping off a cliff after t seconds. What is the height of the diver after 5 seconds?
615 ft