Pre-Algebra: Chapter 11-4
Triangles
Triangles can be classified by their angles or their sides or both. Every angle has 2 acute angles and the 3rd angle can be used to classify the triangle. Triangles always have 180°!
- Acute: has 3 acute angles
- Right: has 1 right angle
- Obtuse: has one obtuse angle
- Equilateral: has 3 congruent sides
- Isosceles: has at least 2 congruent sides
- Scalene: has no congruent sides
Algebra: Chapter 13-1
Introduction to Quadratic Equations
An equation that can be written in the form of ax^2 + bx + c = 0 is a quadratic equation. This is the “standard form”. The solutions of the quadratic equation are called the:
- roots
- solutions
- x-intercepts
- answers
We can factor the equation and use the zero product property to find its solutions. There can be 0, 1 or at most 2 solutions. This is because we have an exponent with power 2 (the ax^2 term).
Equations of the form ax^2 + bx = 0 can be factored by taking out an x leaving us with x(ax + b) and using the zero product property we have x = 0 and ax + b = 0 as solutions.
Equations of the form ax^2 + bx + c = 0 can factored using the BOX METHOD with solutions again arrived at by using the zero product property.
Remember too, the inflexion point (the vertex, the point where the slope of the parabola changes direction) is -b/2a. This can help with the graph if you need to make one.
Purplemath has this link that is pretty good with more explanations and review.