2017­3­29 solve by square roots.notebook
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3/29
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Today's Objective:
Solving Quadratics Using
Square Roots
March 29, 2017
2017­3­29 solve by square roots.notebook
March 29, 2017
What are the solutions to the following equation?
x2 = 25
x = 5 OR x = -5
If x2 = k, the x =
Example
k OR x = - k
(x - 2)2 = 36
x - 2 =
36 OR x - 2 = - 36
Solve each resulting equation.
Exercises 1-4
Solve each equation. Some may have radicals in their solutions.
Remember: Quadratic equations may have TWO solutions.
1. (x - 3)2 = 1
2. 3x2 - 9 = 0
2017­3­29 solve by square roots.notebook
3. 4(x - 3)2 = 1
March 29, 2017
4. 2(x - 3)2 = 12
a. Solve 3x2 − 27 = 0 using square roots.
b. Solve x2 − 10 = −10 using square roots.
c. Solve −5x2 + 11 = 16 using square roots.
2017­3­29 solve by square roots.notebook
Exercise 5
Objectives
What do you notice about the structure
of the quadratic expression in this problem?
How can this structure help us when we
apply this equation?
In this equation, what does the 4 represent?
How would you use this equation to determine
the time it takes the ball to reach the floor?
March 29, 2017
2017­3­29 solve by square roots.notebook
March 29, 2017
Let's look at TWO methods for finding the number of seconds
it takes the ball to reach the ground:
Method 1
Method 2
-16t2 + 4 = 0
2
-16t + 4 = 0
-4(4t2 - 1) = 0
-16t2 = -4
t2 =
t =
t =
1
4
-4(2t + 1)(2t - 1) = 0
___
±√
±
1
2
1
4
2t + 1 = 0 or 2t - 1 = 0
t = -
1
2
1
t =2
2017­3­29 solve by square roots.notebook
March 29, 2017
The surface area S of a sphere with radius r is given by the formula S = 4 r2. Solve the formula for r. Then find the radius of a globe with a surface area of 804 square inches.
Solve the equation using square roots.
1. −3x2 = −75 2. x2 + 12 = 10 3. 4x2 − 15 = −15
2017­3­29 solve by square roots.notebook
March 29, 2017
Solve the equation using square roots.
4. (x + 7)2 = 0 5. 4(x − 3)2 = 9 6. (2x + 1)2 = 36