Day 145

Pre-Algebra: Chapter 11-7

Quadrilaterals

Quadrilaterals are 4 sides figures, their total inside angles add up to 360°. Quadrilaterals are 4 sided figures. There are 3 types of quadrilaterals

  1. Quadrilaterals:have no pairs of parallel lines
  2. Parallelograms: have 2 pairs of parallel sides
  3. Trapezoids: have exactly 1 pair of parallel lines

Parallelograms are further subdivided into types

  • Rectangles: parallelograms with 4 congruent sides
  • Rhombus: parallelograms with congruent sides
  • Square: parallelogram with congruent sides and congruent angles

If 2 figures are similar, then the angles of 1 figure are congruent to the corresponding angles of the other figure. If 2 figures are similar, then their corresponding sides are proportional.

Remember too – a square is rectangle BUT a rectangle is NOT always a square!

Algebra: Chapter 13-4

The Quadratic Formula, finally!

`(−b ± (sqrt(b^2 − 4ac)))/(2a)`

where the a, b and c coefficients are defined by the standard form of the quadratic equation

`ax^2 + bx + c = 0`

This requires that the quadratic equation is always in standard form:

  • a is the coefficient of the `x^2` term
  • b is the coefficient of the x term and
  • c is the constant

Memorize it and memorize the discriminant, the expression under the radical (the `b^2 − 4ac` thingy).

  • If the discriminant is > 0, then there are 2 real number solutions
  • If the discriminant is = 0, then there is just 1 real number solution
  • If the discriminant is < 0, then there are NO real number solutions because you don’t know (yet) how to take the root of a negative real number

Once again, Purplemath.com comes to the rescue, check out these examples for the use of the quadratic formula!

Don’t forget that the

  • solutions
  • answers
  • x-intercepts and
  • roots

all mean the same thing. By definition, the equation `ax^2 + bx + c = 0` implies that we are setting y = 0 and finding the x-intercepts or the roots or the answers or the solutions!!

This entry was posted in Algebra 1, Pre-Algebra. Bookmark the permalink.

Leave a Reply

Your email address will not be published. Required fields are marked *