Assignment 2
Parabolic Transformations
by Emily Bradley
Forms of Parabolic Equations
Standard form  y = ax² + bx + c 
a > 0, parabola opens up a < 0, parabola opens down axis of symmetry: x = b/2a 
Vertex form  y = a(x  h)² + k 
(h, k) is the vertex a > 0, parabola opens up a < 0, parabola opens down  a  > 1, graph narrows  a  < 1, graph widenss 
Intercept form  y = a(x  p)( x  q) 
x interepts are at p and q axis of symmetry between (p,0) and (q,0) 
From vertex to standard form  expand and simplify the binomial 
From standard to vertex form  complete the square 
Conclude 
Graph the parabola y = 2x² + 3x  4
h and k can be calculated using the above formulas giving the vertex form of the equation as
y = 2(x +.75)²  5.125
The following transformations to the original graph occur.
a = 2 
h = .75 
k = 5.125 

