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Math D: 8.1

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.


Example 0.2 4x^2 = 49


Example 0.3 4x^2 + 49 = 0


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

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