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Quadratic Functions

Using forms of quadratic functions: standard, vertex, focus

Three points --> Standard Form Substitute points -- Solve system with matrix
Vertex & Point --> Vertex Form Substitute point and vertex -- Find "a"
Focus & Vertex --> Focus form Substitute "c" -- Substitute vertex
Standard Form --> Vertex Form Use -b/2a to get vertex -- Use "a" value
Vertex Form --> Standard Form Expand the binomial square -- Simplify
Vertex Form --> Focus Form a = 1/4c
Focus Form --> Vertex Form a = 1/4c
Standard Form --> Graph Use -b/2a to get vertex -- "c" is y-intercept -- "a" is stretch factor
Vertex Form --> Graph (h, k) vertex -- "a" is stretch factor
Focus Form --> Graph (h, k) vertex -- "c" is focal length
Standard Form Formula y=ax^2 + bx + c
Vertex Form Formula - Vertical Parabola y=a(x - h)^2 + k
Vertex Form Formula - Horizontal Parabola x=a(y - k)^2 + h -- be careful of (h, k) placement
Focus Form Formula - Vertical Parabola y=1/4c(x - h)^2 + k
Focus Form Formula - Horizontal Parabola x=1/4c(y - k)^2 + h -- be careful of (h, k) placement
Created by: lajerauld