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QUADRATIC FUNCTION SUMMARY

QUADRATIC FUNCTION SUMMARY
STANDARD FORM: f(x) = ax^2 + bx + c
  Domain Graph
(shape)
Vertex Range yintercept xintercept(
s)
a > 0 all
real
numbers *
Lowest
point
(-b/2a, f(-b/2a)
f(-b/2a) to
infinity
(0, c) solutions to
f
(x) = 0
a < 0 all
real
numbers *
Highest
point
(-b/2a, f(-b/2a)
negative
infinity to
f(-b/2a)
(0, c) solutions to
f
(x) = 0
VERTEX FORM : f(x) = a(x – h)^2 + k
a > 0 all
real
numbers*
(h, k) k to infinity (0, ah^2 +k) solutions to
f(x) = 0
( Use square
root solution
method )
a < 0 all
real
numbers*
(h, k) negative infinity
to k
(0, ah^2 +k) solutions to
f(x) = 0
( Use square
root solution
method )
* A quadratic function used as a physical model may have restrictions.
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