Name ________________________________
Bartlett
Algebra I - _____
Date _________________________________
CW 14-2: The Quadratic Formula
Important Information/Examples:
If ax2 + bx + c = 0, and a ≠ 0, then
!!± ! ! !!!"
𝑥=
.
!!
The restriction a ≠ 0 is needed for two reasons:
1. If a were 0, then the equation would not be a quadratic.
2. If a were 0, then the denominator would be 0.
Solve the using the Quadratic Formula.
1)
5x2 + 12x + 3 = 0
2)
5x2 + 13x – 6 = 0
3)
7x2 – 3x + 6 = 0
Wrap Up:
How does the discriminant help in using the Quadratic Formula?
HW 14-2: The Quadratic Formula
Solve the following problems. Show all of your work and circle your answers.
Answer in complete sentences where appropriate.
High School Placement Problems:
1)
Find the slope of the line 2y = 8x − 3.
2)
Josh earns money by washing cars in his neighborhood. He spent $215 on
supplies and charges $15 for each car washed. Josh’s profit, p , can be
represented by the function p = 15n − 215, where n represents the number of
cars that Josh washes. What is the minimum number of cars Josh must wash to
make a profit?
3)
Which expression is equivalent to − 7(x − 2) + 5(3 − x ) − 4x ?
4)
In the equation 6.5x + 1.4y = 59, what is the value of x when y = 5?
5)
A quadratic function is given. f (x ) = 3x 2 − x + 6 What is f(2)?
Quadratic Formula Problems:
Solve the equation using the Quadratic Formula. Write irrational solutions as
decimals, correct to two decimal places.
6)
7x2 – 20x + 9 = 0
7)
5x2 – 13x + 12 = 0
8)
3x2 – 24x + 17 = 0
9)
5x2 – 13x – 6 = 0
10) 6x2 + 9x + 10 = 0
11)
0.2x2 – 6.7x + 2.1 = 0
12)
0.2x2 – 0.8x – 4.2 = 0
13) 5x2 – 9 = 0
14) 6x2 + 7 = 0
15)
x2 – x = 0
16) 3x2 + 5x = -2
17)
x(x – 3) = 7
2
18) (x + 3) + 2x = 2
19) (3x – 2)(2x + 5) = 36
2
2
20) (x + 10) + 5x = (x + 3) - 20
Key:
1)
6)
11)
16)
x = 5 points each
4
2)
15
2.30, 0.56 7)
𝜙
35, -1.5
12)
7, -3
!
− !, -1
17)
4.54, -1.54
3)
8)
13)
18)
-16x + 29
7.21, 0.79
1.34, -1.34
-1, -7
4)
9)
14)
19)
8
3, -0.4
𝜙
2, -3.83
5)
10)
15)
20)
16
𝜙
1, 0
-6