Describe and explain the transformation of the parent graph 𝑦𝑦 = 𝑥𝑥 2 to 𝑓𝑓(𝑥𝑥) = 2(𝑥𝑥 + 2)2 − 3.
Quadratic function – any function that can be written in the form 𝑓𝑓(𝑥𝑥) = 𝑎𝑎𝑥𝑥 2 + 𝑏𝑏𝑏𝑏 + 𝑐𝑐, where 𝑎𝑎 ≠ 0. Vertex form – any quadratic function written as 𝑓𝑓(𝑥𝑥) = 𝑎𝑎(𝑥𝑥 − ℎ)2 + 𝑘𝑘, where 𝑎𝑎 ≠ 0.
Axis of symmetry –a line that divides the parabola into two mirror images, the equation for an axis of symmetry is 𝑥𝑥 = ℎ.
Vertex of the parabola –the intersection of the parabola and its axis of symmetry is (ℎ, 𝑘𝑘). 5
y
4
3
2
1
x −4
−3
−2
−1
1 −1
𝑦𝑦 = 𝑥𝑥 2
2
3
4
Graphing a Function of the form f(x) = ax2 EX #1: Graph
𝒇𝒇(𝒙𝒙) = 𝒂𝒂(𝒙𝒙 − 𝒉𝒉)𝟐𝟐 + 𝒌𝒌
y
𝑦𝑦 = 2𝑥𝑥 2
If 𝒂𝒂 > 0, then _________________________________
Vertex: _______________ Axis of Symmetry: ____________________
x
Point: __________________
Vertex: _______________ Axis of Symmetry: ____________________
Point: __________________
Reflected Point:_____________
If 𝒂𝒂 < 0, then _________________________________ (𝒉𝒉, 𝒌𝒌) is _______________________________________
𝒙𝒙 = 𝒉𝒉 is _______________________________________