Download Unit 3: Equations - Math Specialist Aman

Unit 3: Quadratic Equations
Unit Review
Topics Covered:
1. Factoring
 GCF
 Difference of Squares
 Easy and Hard Trinomials
 Substitution
 3 and 1 Grouping
2. Solving Equations by Factoring
3. Solving Equations by Completing the Square
4. The Quadratic Formula: x 
 b  b 2  4ac
2a
5. The Discriminant: b 2  4ac
 If b 2  4ac > 0, we have 2 different real roots
 If b 2  4ac = 0, we have 2 equal real roots
 If b 2  4ac < 0, we have no real roots
Homework:
p. 242-248
Examples:
1. Factor
a) 8 y 2  22 yx
b) x 2 (b  a)  4(b  a)
c) 5 x 4  80
d) x 2  12 xy  20 y 2
e) 3x 2  10 x  8
f) 2a 5  26a 3  72a
g) 12 x 3  6 x 2 y  18xy2
h) (3a  5) 2  (a  3) 2
i) (2 x  1) 2  5(2 x  1)  6
j)
k) x 2 
9
5
x
2
2
1 2 2
1
x  x
5
15
3
l) x 2  10 x  25  z 2
2. Solve by completing the square:
a) 2 x 2  12 x  5
b) 2 x 2  10 x  5
3. Solve. You may use the quadratic formula if appropriate:
a) (2 x  1)( x  3)  ( x  2) 2
b)
x  27  3  x
4. Find the value of the discriminant, then state the nature of the roots:
a) 3 x 2  5 x  2
b) 4 x 2  12 x  9
5. Find k so that the following has no real roots:
5 x 2  kx  3  0
6. A stone is thrown off of a 30 m cliff. It’s height is given by the formula:
h  4.9t 2  10.5t  30 . How long does it take to reach the bottom of the cliff?
7. When 3 times a number is subtracted from the square of the number the result is 28.
Determine the number
8. Two numbers have a sum of 20 and a product of 84. Determine the numbers.