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3.1 Quadratic
Functions
Quadratic Functions
A quadratic function is a function of the form:
f (x)  ax  bx  c
2
where a, b, and c are real numbers and a ≠ 0.
 Vertex form of a quadratic equation:
2
f (x)  a(x  h)  k
A quadratic function can be written in vertex

form by completing the square.
Graphing Quadratic Functions
Graph the following function by completing the square.
f (x)  3x 2  12x  1
Finding Quadratic Equations
Determine the quadratic equation in standard form whose
vertex is (4,-1) and passes through the point (2,7).
Graphing Quadratics by Hand
1) Determine the axis of symmetry.
x
f (x)  3x 2  12x  1
b
2a
2) Determine the vertex.

3) Determine the y-intercept.
4) Determine an additional point using symmetry.
5) Plot the points and draw the graph.
Quadratic Functions
Determine the following for the quadratic function:
f (x)  2x 2  8x  3
1. Opens up or down
2. Maximum or Minimum
3. Axis of Symmetry
4. Vertex
5. y-intercept
6. x-intercept(s)
7. Domain
8. Range
9. Increasing Interval
10. Decreasing Interval

Applications of Quadratic Functions
A suspension bridge has towers 80 feet above the surface of the
road and 500 feet apart. Cables attached to the top of the towers
form a parabolic curve that touches the road surface in the middle
of the bridge. Find the height of the cable 125 feet from the
center of the bridge.
Applications of Quadratic Functions
A farmer with 4000 meters of fencing wants to enclose a
rectangular plot that borders a river. If the farmer does not fence
the side along the river, what is the largest area that can be
enclosed with the fencing?
3.1 Quadratic
Functions
Homework:
pgs. 164 – 166
#23 – 29 odd, 45 – 51 odd, 55,
57, 77, 81 (no e), 103