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 |
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| 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 |
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