1. Solving Quadratic Equations by Finding Square Roots
Objective:
Students will solve a quadratic equation by
finding square roots.

3. Algebra Standards: 2.0 Students understand and use such operations as
taking the opposite, reciprocal, raising to a power,
and taking a root. This includes the understanding
and use of the rules of exponents.
15.0 Students apply algebraic techniques to rate
problems, work problems, and percent mixture problems.
23.0 Students apply quadratic equations to physical problems,
such as the motion of an object under the force of gravity.

4. is an equation that can be written in
Vocabulary
Quadratic Equation
is an equation that can be written in
the standard form ax + bx + c =0, where
a ≠ 0. 2
If d > 0, then x = d has two solutions: x = 2
If d = 0, then x = d has one solutions: x = 0 2
If d < 0, then x = d has no real solutions. 2

5. Vocabulary
when x = 3
when x = -3
when x = -3

6. a) p = 225 c) k = 15 x = 16 b) x = 16 p = 225 k = 15 | x | = 4 | p | =
#1 Solve Quadratic Equations
Solve each equation 2 2 2 a) p
= 225 c) k
= 15 x
= 16 b) 2 2 2 x
= 16 p
= 225 k
= 15
| x | = 4
| p | = 15
| k | = x = ±4 p =
±15 k = 2 2 d) e) x
= -4 x
= 0
No real solution
x = 0

7. a) b) x + 7 = 16 3x – 10 = 65 -7 -7 +10 +10 x = 9 3x = 75 | x | = 3 x
#2 Rewrite Before Finding Square Roots
Solve each equation 2 2 a) b) x
+ 7 = 16 3x
– 10 = 65 -7 -7
+10
+10 2 1 2 x = 9 3x = 75
| x | = 3 x = ±3 2 x = 25
| x | = 5 x = ±5

8. c) d) x + 7 = 5 (x + 1) = 16 -7 -7 (x + 1) = 16 x = -2 | x + 1 | = 4
#2 Rewrite Before Finding Square Roots
Solve each equation 2 2 c) d) x
+ 7 = 5
(x + 1) = 16 -7 -7 2
(x + 1) = 16 2 x = -2
| x + 1 | = 4
No solution x
+ 1 = 4 x
+ 1 = -4 -1 -1 -1 -1 x = 3 or x = -5

9. e) (a – 4) = 81 (a – 4) = 81 | a – 4 | = 9 a – 4 = 9 a – 4 = -9 +4 +4
#2 Rewrite Before Finding Square Roots
Solve each equation 2 e)
(a – 4) = 81 2
(a – 4) = 81
| a – 4 | = 9 a
– 4 = 9 a
– 4 = -9 +4 +4 +4 +4 a = 13 or a = -5

10. For a falling object, you can estimate/find the height of it.
Falling Object Model
For a falling object, you can estimate/find the
height of it. 2
h = -16t + s
h = height of the object in feet (ft)
16 ≈ Acceleration due to gravity ( ft/ sec ) 2
s = initial drop height (ft)

11. Solution: = -16 t + 400 h = -16t + s t = ? h = 0 ft s = 400 ft 5 =
#Use a Falling Object Model
If a penny is drop from the 5th floor of a building which
is 400 ft above ground, how long will it take to hit the ground.
Solution: 2 =
-16 t
+ 400 2
h = -16t + s
–400
–400 1 2
t = ?
-400 =
-16t
h =
0 ft 2 25 = t
s =
400 ft 5 =
| t | t =
5 seconds
± 5 = t

12. Assignment
Book Pg. 508 – 509
# 34 – 48 all
#59, 60