Linear/Quadratic Equations
2x+5. Solve for X
x=-2.5
Graph 1
D: ( - inf, inf)
R: ( -inf, inf)
sqrt(-81) = ?
9i
3 + 3 + 3i + 4i
6 + 7i
The height of a flare fired from the deck of a ship in distress can be modeled by h= t2 - t + -56, where h is the height of the flare above water and t is the time in seconds. Find the time it takes the flare to hit the water.
t = 7 s
x2-25. Solve for X
x=-5,5
Graph 2
D: ( -inf, inf)
R: {3}
sqrt(x+18)=x-2
x=7, x=-2
(extra 100: are there any false answers here?)
7i ⋅ 3i(−8 − 6i)
7i ⋅ 3i(−8 − 6i)
A relief package is released from a helicopter at 1600 feet. The height of the package can be modeled by the equation h= -16t2 + 1600 , where h is the height of the package in feet and t is the time in seconds. The pilot wants to know how long it will take for the package to hit the ground.
10 s
(extra credit: what was your other answer and why does it not work?)
using points (1, 15) and (2, 18), find your y=mx+b equation and solve for x.
x=4
Graph 3
D: (-inf, 2)
R: [-3, inf)
Use the difference Quotient to solve.
f(a)= 4a - a2
4 - 2a - h
(1 − 7i)2
−48 − 14i
Quadratic Problem: A football is kicked straight up from a height of 3 feet with an initial speed of 54 feet per second. The formula h =- 16t2 + 54t + 3 describes the ball's height above the ground, h, in feet, t seconds after it was kicked. How long will it take for the football to hit the ground?
t = 3.4ish
3x2+11x+6=0, Solve using the AC method. Leave your answer as a fraction if you get one.
(3x+2)(x+3)
x=-3,-2/3
Graph 4
D: (-inf, -1) U (1,3)
R: (-inf,1)
Solve the equation by taking the square root :
(x-4)2-16=0
x = 0 and x=8
6(−7 + 6i)(−4 + 2i)
96 − 228i
Rational Problem: Fran can clean a garage in 3 hours. Her friend Robin can clean it in 4 hours. How long would it take them to clean the garage if they work together? (Hint: How much work can each get done in an hour?)
12/7 or 1.7
2x2-5x+3 using the quadratic formula, find x.
x=3/2, x=1
Graph 5
D: {-2, 2}
R: (-inf, inf)
Using the Difference Quotient,(f(x-h)-f(x))/h , find the answer for x^2-4
2x+h
(−2 − 2i)(−4 − 3i)(7 + 8i)
−98 + 114i
Quadratic Problem: A pool measuring 22 meters by 30 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 2100 square meters, what is the width of the path?
10 m