10.1!

10.1 The Square Root Property and Completing the Square

-the square root property allows you to eliminate the squared property of a number.

a means, “what two of the exact same number can be multiplied to get a?”

Ex. x^2=36

x^2= 36

x= 6 and x=-6

Because 6x6=36 and -6x-6=36

Standard Form of Quadratic Equation

ax^2+bx+c=0

A quadratic equation is a second degree equation because the term with the largest sum of exponents is ax^2 and its exponent is 2.

Ex. 4(x^2)+(-48x)+8=0

2(x62)+36x+6=0

Zero Factor Property

That is, if ab=0, then a=0 or b=0.

(3x+7)(x-4)=0

(a) x (b)=0

Either quantity a has to equal zero or quantity b has to equal zero in order for this statement to be true.



Properties of Square Roots, only used if a is greater than or equal to zero or b is greater than or equal to zero.


Ex. Simplify the following radical.
20 *Find the largest perfect square that goes into 20 evenly.

20=
4x5= 4x5= 25

Solve a quadratic equation in the form (ax^2+b)^2=c

Ex. (x-5)^2=36
(x-5)2= 36
((x-5)2)= 36
(x-5) =6 or (x-5)=-6
x=11 or x=-1
0 the square root could be positive or negative.