9.2
Characteristics of Quadratic Functions
Finding Zeros of Quadratic Functions:
A zero of a function is an x-value that makes the
function equal to 0.
So a zero of a function is the same as an x-intercept.
y = x2 - x - 2
y = -2x2 + 4x - 2
y = 1 x2 + 1
4
Finding the Axis of Symmetry by Using Zeros:
If there is one zero:
y = -2x2 + 4x - 2
If there are two zeros:
Finding the Axis of Symmetry by Using the Formula:
The axis of symmetry is the vertical line
x =
-b
2a
Find the axis of symmetry for the graph of
y = 2x2 + x + 3
Find the axis of symmetry for the graph of
y = -3x 2 + 10x + 9
Find the axis of symmetry for the graph of
y = 5x2 + 8
Finding the Vertex of a Parabola:
The vertex of a parabola will always be on the axis
of symmetry, so first find the axis of symmetry.
Example: y = x2 - 4x - 10
Step 2: To find the corresponding y-coordinate, substitute
the x-coordinate of the vertex (the axis of symmetry) into
the function.
The graph of f(x) = -0.06x 2 + 0.6x + 10.26 can be used to
model the height in meters of an arch support for a bridge,
where the x-axis represents the water level and
x represents the distance in meters from where the arch
support enters the water.
Can a sailboat that is 14 meters tall pass under the bridge?
Explain.