Quadratic Formula + Word Problems
Find the Discriminant to determine the number of solutions
2x2-2x-4=0
36, 2 real solutions
Rewrite each equation as a system of equations and then use a graph to solve.
x2-6x=2x-16
(4, -8)
x2+4x+3
x = -3
x = -1
x2-2x-15=0
x= -3
x= 5
Simplify:
4Sqrt(84x5)
8x2Sqrt(21x)
Solve using the quadratic Formula:
2x2-2x-4=0
x = -1
x = 2
Find the solution of the system of equations:
y=-4x2+x+1
y=-7x+1
(0,1) and (2, -13)
Solve by graphing:
0=x2+6x+9
x = -3
Solve by factoring:
x2+10x+25 = 0
x = -5
Simplify:
Sqrt(35x) Sqrt(21x)
7x Sqrt(15)
Solve using the quadratic Formula:
x2-6x=-7
x = 4.41
x = 1.59
Find the solution to the system of equations:
y = x2+6x+9
y = 3x
No solution
Solve by graphing:
-4x2=3
No real solutions
Solve by factoring:
2x2 - 2x - 4=0
x = -1
x = 2
Solve using Square Root Method:
x2=-100
No real solutions
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 ft per second, then its height h after t seconds is given by the equation h(t) = -16t2+128t. What is the max height, and how long will it take the rocket to reach the max height?
Max Height: 256 ft.
Time to reach Max Height: 4 seconds
Since opening day, attendance at Pool A has increased steadily while attendance at Pool B first rose then fell. Equations modeling the daily attendance (y) and number of days since opening day (x) are shown:
Pool A: y=28x+4
Pool B: y=-x2+39x+64
On what day was the attendance the same at both pools?
Day 15
x2+5=6x
x = 1
x = 5
Solve by factoring:
3x2-6x=24
x = -2
x = 4
Solve using Square Root Method
5x2+10=330
x = +/- 8
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 ft per second, then its height h after t seconds is given by the equation h(t) = -16t2+128t. After how many seconds will the rocket be 112 feet above the ground?
t = 1 second and t = 7 seconds
The equations below model the numbers of two portable music players sold (y) and days after both players were introduced (x).
Music Player A: y = 191x – 32
Music Player B: y = ‐x2 + 200x + 20
On what day(s) did the company sell the same number of each player? And how many were sold?
Day 13
2451 Sold
Solve by graphing:
-4x2=64 - 32x
x = 4
A picture inside a frame has an area of 375 cm2. What is the width, x, of the frame if the length is 30 cm. by 20 cm.
2.5 cm.
Solve using Square Root method:
2(x-8)2-5 = 283
x = 20
x = -4