** Property 0.1 A** few points to review.

•A quadratic equation in x can be written in the standard
form

•Some equations can be solved by factoring .

•A polynomial function of the form

is **a quadratic function**. These are shaped like
bowls or inverted bowls.

•The real solutions of ax^2 +bx+c = 0 correspond to the
x- intercepts for

the corresponding graph .

**Property 0.2** If u is an algebraic expression and d
is a nonzero real number ,

then u^2 = d is equivalent to

Equivalently if u^2 = d, then

Note that we write as short hand for + and -. Whenever you
see

think of it as

**Example 0.1** 5x^2 = 20

means x = 2 or x =-2.

**Check:**

**Example 0.2** 4x^2 = 49

**Check:**

**Example 0.3** 4x^2 + 49 = 0

**Check:**

**Example 0.4** (x-5)^2 =-4

Recall if u^2 = d, then

In this example u = (x-5) and d =-4.

**Property 0.3** If x^2 + bx is a binomial , then by
adding which is the

square of half the coefficient of x, a perfect square trinomial will result.

Whenever adding to one
side of the equation, make sure to add to
the other side as well.

**Example 0.5** x^2 + 6x = 7

The solution set is {-7, 1}.

**Example 0.6 **x^2 + 8x - 5 = 0

The solution set is

If the coefficient of the x^2 term is not equal to 1, then
divide the entire

equation by that coefficient.

**Example 0.7** 2x^2 + 5x - 3 = 0

The solution set is

**Example 0.8** 9x^2 - 6x + 5 = 0

The solution set is