Algebra Unit 12 REVIEW
(not worth points)
Name ___________________________
12.1 Solve Quadratics by Square Roots:
Solve each equation. Recall that those with an x2 will have two solutions. SHOW ALL WORK.
Give exact answer.
1. (x – 6)2 = 144
2. 5(x + 7)2 = 80
3. 1 x 2  7  12  20
4
12.2 Solve by Completing the Square:
Fill in the blanks to write the function as binomial squares and find the missing c value.
4. x2 + 14x + _____
5. x2 – 9x + ____
(x + ___)2
(x – ___)2
Solve by completing the square. Show all work. Give exact answer only.
6. x2 + 2x – 63 = 0
7. x2 – 12x + 13 = 0
12.2 Complete the Square – Vertex Form:
Write each quadratic function in vertex form. Give the coordinates of the vertex and the axis of
symmetry. Then tell whether the vertex is a maximum or a minimum.
8. f(x) = x2 + 18x – 12
9. f(x) = x2 – 4x – 23
12.3: The Discriminant:
Find the discriminant and tell the number and type of solutions.
10. 8x2 – 2x + 9 = 0
11. –6x2 + 16x + 28 = 0
12. Eva is jumping on a trampoline. Her height h in feet can be modeled by the equation
h = –16t2 + 3.8t + 2.5, where t is time in seconds. Use the discriminant to determine if Eva will ever
reach a height of 15 ft. EXPLAIN your answer.
12.4 The Quadratic Formula: Solve the following by using the Quadratic formula.
13. –4x2 – 12x + 16 = 0
14. n2 – 6n = 7
12.5 Height Equations and Other Application Problems:
15. Elias hits a baseball into the air. The equation h = –16t2 + 24t + 3 models the height h in feet of
the ball after t seconds. Use the quadratic formula to find out how long the ball was in the air.
Round your answer to the nearest hundredth.
16. Create a quadratic equation that has solutions of 2 and –7. Leave in factored form.
17. Use the falling-object model h = –16t2 + h0 where t is measured in seconds and h is measured in
feet to find the time required for an object that is first dropped from a height of h0 = 150 feet and
then from a height of h0 = 300 feet. Does an object that is dropped from twice as high take twice as
long to reach the ground? Explain your answer. Round to the nearest hundredth.
h0 = 150 ft ____________
h0 = 300 ft ______________
18. A package of supplies is dropped from a helicopter hovering 300 meters above the ground. The
attached parachute fails to open. The equation h = –4.9t2 + 300 models this situation. After
how many seconds will the package reach the ground? Round to the nearest hundredth.
19. Suppose a ball is thrown straight up from a platform that is 8 feet above the ground, and the initial
velocity of the ball is 25 feet per second. The equation h= –16t2 + 25t + 8 describes the relation
between the ball’s height above the ground and time.
a) What is the height of the ball after 1 second?
b) When does the ball hit the ground? Round to the nearest hundredth.
20. The length of a standard basketball court is 44 ft longer than the width.
a) Write an expression for the area of the field.
b)
The area of the court is 4700 square feet. Find the dimensions.
Answers: 1. 18 & -6 2. -3 &-11 3. 5 & -5 4. (x + 7)2, 49 5. (x – 9/2)2, 81/4 6. 7 & -9 7. 6  23
8. f(x) = (x + 9)2 – 93, (-9, -93), x = -9, min 9. f(x) = (x – 2)2 – 27, (2, -27), x = 2, min 10. -284, 0 real, 2 complex
11. 928, 2 real 12. -785.56, A negative discriminant means there is no real solution to the problem. 13. -8 & 1
14. 7 and -1 15. 1.62 sec 16. y = (x – 2)(x + 7) 17. 3.06 sec, 4.33 sec , no it is only 1 additional second not twice as much.
18. 7.8 sec 19. 17 feet, 1.83 sec 20. w(w + 44), 50 feet by 94 feet