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
- Quadrilaterals:have no pairs of parallel lines
- Parallelograms: have 2 pairs of parallel sides
- 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!!