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Chapter 1 - Coggle Diagram
Chapter 1
Graph (Parabola)
Minimum point
when 𝑎 > 0
Maximum point
when 𝑎 < 0
Vertex
( -b/2a, f(-b/2a))
Line of symmetry
x = -b/2a
Intercepts
x-intercepts (roots), y intercept (when x=0)
Methods to Solve
Completing the Square
Quadratic Formula
Factorisation
Quadratic Inequalities
Discriminant
0
Two distinct real roots
= 0
Two equal real roots
< 0
No real roots
Intersections
Two points of intersection
two solutions
One point of intersection
tangeant
No intersection
no real solution
Tangeant
Touches the parabola at exactly one point
Has the same slope as the parabola at that point
Quadratics
Factorisation
Write as product of factors
Introduced by Babylonians
Developed by Al-Khwarizmi
Conic
Circle, Ellipse, Parabola, Hyperbola