Name: ________________________________________
Algebra 1 PMI
Quadratics HOMEWORK PACKET
Standard form and the axis of symmetry
Find the axis of symmetry and rewrite in standard form if necessary.
1. y= x2 +2x -8
4. -5x - 4 = 2x2
2. -x2 - 3x = 2
5. y= 3x2 -2x
3. y= x2 -5x -1
Transforming Quadratic Functions
Does the graph of the given equation open up or down? Is the graph wider or narrower than the parent
equation of y=x2? What is the y-intercept?
1. y =-.6x2 +3x -6
4. y = 1.3x2 +4x
2. y = 1.7x2 -4x +5
5.
3.
y = -1.02x2 +8
y = 5x2
Graphing to Find Zeros
Find the zeros of the following quadratics:
1.
y
8
6
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-2
-4
-6
-8
2.
y
8
6
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-2
-4
-6
-8
3. y = x2 -6x +5
7. y = x2 +2x +4
4. y = -x2 +3x +10
8. y = 2x2 +5x +2
5. y = x2 +6x +9
9. y = -3x2 +11x +4
6. y = x2 +x -12
Solving by Factoring
Solve the following quadratics by factoring.
1. a2 +6a +5= 0
6. f2 +6f +9 = 0
2. b2 -b -6= 0
7. –g2 +7g = 6
3. c2 -6c = -8
8. 2h2 +8h +6= 0
4. d2 +7c = -10
9. 3j2 -7j = -4
5. -e2 +16 = 0
10. A garden has a length of (x - 4)feet and a width of (2x +3)feet. The garden’s total area is 76 square
feet. Find the length.
Solving Using the Square Roots Method
Solve the following quadratics using the square roots method.
1. m2 = 36
4. 5q2 = 20
2. n2 = 64
5. r2 -3 = 13
3. 3p2 = 27
6. s2 +8 = 24
7. 2t2 -6 = 12
9. (v -2)2 +4 = 13
8. 3u2 +5 = 8
10. 3(w +4)2 -4 = 44
11. Two times the square of five more than a number is seventy-two. Write an equation that models this
situation. Solve the equation.
Solving by Completing the Square
Fill in the blank to complete the square.
1.
a2 + 12a +__
4.
d2 - 16d +__
2.
b2 + b +__
5. e2 + 9e +__
3.
c2 - 14c +__
6. f2 - 1f +__
Solve the following quadratics by completing the square.
7. h2 + 4h =12
11. 2n + 80= -n2
8. j2 - 10j = -9
12. 6p + p2 = 0
9. k2 + 13 = -14k
13. 2q2 - 12q = -22
10. m2 - 21 = 20m
14. 3r2 + 15r = 18
15. A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as
h = -16t2 + 160t until it hits the ground. At what time(s) is it at a height of 9 feet above the
ground?
Solving Using the Quadratic Formula
Solve the following using the quadratic formula. Round answers to the hundredth place.
1. x2 +7x -5 =0
4. -3m2 + 4m = -5
2. g2 -5g +3 =0
5. 5w2 -2 = 5w
3. 2d2 + 5d -3 =0
6. 3z – 6z2 = -8
7.
An employee makes (3x - 5) dollars an hour for x hours. If the employer wants to pay no more
than $200 a day, what is the maximum number of hours the employee can work? (Round to the
nearest quarter hour)
Discriminant
Find the discriminant for each quadratic equation. State the number of real roots and then find the real
solution(s), if any exist.
6. 3x2 - 9x + 7 = 0
10. 5x2 = 7x – 6
7. 2x2 - 4x + 2 = 0
11. 3x2 - 7x – 8= 0
8. 5x + 7x2 + 8 = 0
12. (x + 3)(2x + 6) = 11
9. 7x – 6 = 2x2
13.
A rock is thrown with a height equation of h = -16t2 + 64t + 5 (where h is the height of the rock in
feet at any given time of t in seconds). Will it reach a height of 50 feet? Explain your answer.
Mixed Application Problems
Solve the following problems using any method.
1.
The product of two consecutive positive integers is 272, find the integers.
2.
The product of two consecutive positive even integers is 342, find the integers.
3.
The product of two consecutive odd integers is 483, find the integers.
4.
Two planes leave airport at the same time (from different runways). If three hours later they are
600 miles apart and the plane flying south has traveled 100 miles farther, how far did the one
flying west travel?
5.
Two cars leave a gas station at the same time, one traveling north and one traveling east. One
hour later they are 90 miles apart and the one traveling east went 15 miles farther, how far is it
from the gas station?
6.
A square has its length increased by 6 feet and its width by 8 feet. If the resulting rectangle has
an area of 239.25 square feet what was the perimeter of the original square?