Show:
Factoring
Square Roots
Application: Roots (DOUBLE)
Quadratic Formula
Application: Min & Max (DOUBLE)
100
Use the Zero Product Property to solve the following quadratic equation. (2x - 7)(x + 2) = 0
x = 7/2 x = -2
100
Solve the following quadratic equation by using square roots: x^2 = 4
x = 2 x = -2
100
An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t^2 + 19.6t + 58.8, where s is in meters. When does the object strike the ground?
t = 6 seconds
100
What is the quadratic formula?
x = -b +- sqrt(b^2 - 4ac) 2a
100
An object is launched from ground level directly upward at 39.2 m/s. State the function that represents the situation where h(t) is the height in meters over time, t, in seconds.
h(t) = –4.9t^2 + 39.2t
200
Solve the following quadratic equation by factoring. x^2 + 3x + 2 = 0
x = -2 x = -1
200
Solve the following quadratic equation by using square roots: (x+3)^2 = 7
x= -3 +/- rad7
200
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. State the equation that models the situation, where h(t) is the height after t seconds.
h(t) = –16t^2 + 64t + 80
200
Solve the following quadratic equation by using the quadratic formula: 4x^2 - 17x - 15 = 0
x = 5 x = -3/4
200
A football is kicked into the air. Its height in meters after t seconds is given by h=-4.9(t-2.4)^2+29. What was the maximum height of the ball?
The max height is 29 m (reached after 2.4 sec).
300
Solve the following quadratic equation by factoring. 7x^2 + 35x - 42 = 0
x = -6 x = 1
300
Solve the following quadratic equation by using square roots: (x+ 1/8)^2 = 49/64
x = 3/4 x = -1
300
When a home-made rocket is launched from the ground, it goes up and falls in the pattern of a parabola. The height, in feet, of a home-made rocket is given by the equation h(t)=160t−16t2 where t is the time in seconds. How long will it take for the rocket to return to the ground?
The rocket will hit the ground after 10 seconds.
300
Solve the following quadratic equation by using the quadratic formula: 9x^2 + 6x -11 = 0
x = (1 +/- 2rad3)/3
300
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What will be the object's maximum height? When will it attain this height?
It takes two seconds to reach the maximum height of 144 feet.
400
Solve the following quadratic equation by factoring. 3x^2 - 8x = 16
x = -4/3 x = 4
400
Solve the following quadratic equation by using square roots: 3(x-1)^2 +5 = 24
x = 1 +/- rad3
400
The number of softball games that must be scheduled in a league with n teams is given by G(n)=n2−n2. Each team can only play every other team exactly once. A league schedules 21 games. How many softball teams are in the league?
There are 7 teams in the softball league.
400
Solve the following quadratic equation by using the quadratic formula: 8x^2 + 6x + 5 = 0
x = (-3 +/- i rad31)/8
400
The observed bunny rabbit population, p, on an island is given by the function p(t)=-0.4t^2+130t+1300, where t is the time in months since they began observing the rabbits. (a) When is the maximum population attained, and (b) what is the maximum population?
The maximum rabbit population was 11762 rabbits (we can’t have half of a rabbit!) when it was 162.5 months after they began observing the rabbit population.
500
Solve the following equation by factoring. 4x^3 - 10x^2 - 6x = 0
x = -1/2 x = 0 x = 3
500
Solve the following quadratic equation by using square roots: 5(x+2)^2 + 13 = 20
x = -2 +/- 3i
500
An object is launched from ground level directly upward at 39.2 m/s. For how long is the object at or above a height of 34.3 meters?
The object is at or above 34.3 meters for six seconds.
500
Solve the following quadratic equation by using the quadratic formula: x^2 +(rad3)x +3 = 0
x = (-rad3 +/- 3i)/2
500
You have a 500-foot roll of fencing and a large field. You want to construct a rectangular playground area. What are the dimensions of the largest such yard? What is the largest area?
The largest area will have dimensions of 125' by 125', for a total area of 15 625 square feet.