4/3/2017
Solving Quadratic Equations
by Finding Square Roots
How would you solve the equation:
x2 = 4
(take the square root of each side!)
* Remember, the square
root of a positive # has
2 answers! (one + and
one -)
Properties of Square Roots
RADICAL
3
RATIONAL EXPONENT
(a>0 and b>0)
1. Product Property –
2. Quotient PropertyExample:
RADICAL
SIGN
RADICAND
Examples
1.
2.
3.
Example:
Rationalizing the Denominator
You CANNOT leave a radical in the
denominator of a fraction!
No tents in the basement!!!!
(the numerator is OK)
Just multiply the top & bottom of the fraction
by the radical to “rationalize” the
denominator.
1
4/3/2017
More Examples!
Solving Quadratic Equations
1. Solve. 3 - 5x2 = -9
-3
-3
-5x2 = -12
-5
-5
2
x =
1.
Can’t have a tent in the
basement!
2. Solve. 3(x-2)2=21
3
3
(x-2)2 = 7
2.
Falling Objects!
More Examples!
3. Solve. 4x2-6=42
+6 +6
4x2=48
4
4
x2 = 12
• Use h = -16t2 + h0
4. Solve.
Height
of the
object
after it
has
fallen
# of seconds
after the
object is
dropped
Object’s
initial
height
Example
• The tallest building in
the USA is in
Chicago, Illinois. It is
1450 ft. tall. How
long would it take a
penny to drop from
the top of the building
to the ground?
2