Properties of Quadratics
Finding the domain and range of a
quadratic function is as easy as looking at
the graph.
Remember that the:
1) domain is the collection of all input values (x values)
2) range is the collection of all output values (y values)
Domain: -∞<x<∞
Range: -4≤y<∞
Line of symmetry - divides the parabola
into mirrored images, it is always a
vertical line with the equation x = n.
x=1
x-intercept - x-value where a graph
crosses the x-axis. NOTE: In quadratic
equations we also call these roots,
solutions, and zeros.
x-int = {-1, 3}
y-intercept - y-value where a graph
crosses the y-axis. Remember to find the
y-intercept you can always plug 0 in for x.
y-int = -3
vertex - the maximum or minimum (y)
value on a parabola.
vertex = (1,-4)
Properties of Quadratics
Functions can be even, odd, or neither.
An even function gives the same value when
you plug in opposite numbers.
An odd function gives the opposite value
when you plug in opposite numbers.
If plugging in opposite numbers, a function
could also be neither if the value is not the
same or opposites.
Decide whether the following functions are even, odd, or neither.
1) y = 4x2
2) y = 3x3 - 7x
4) y = -4x2 - 8
5)
EVEN
y = -x2
EVEN
3) y = -3x
6)
y = -x2 + 2x -1
NEITHER
State the domain and range of the
following functions.
1.
2.
Domain: -∞<x<∞
Range: 2≤y<∞
Solution(s): No Real Solution
3.
Domain: -∞<x<∞
Range: -∞<y≤1
x-int(s): x={1,3}
Domain: -∞<x<∞
Range: 0≤y<∞
Root(s): x=0
4.
Domain:
Range:
Zero(s):
-∞<x<∞
-∞<y≤4
x={-3,1}