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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 using tranformations.
f (x)  3x 2  12x  1
Finding Quadratic Equations
a) Determine the quadratic equation in standard form whose
vertex is (4,-1) and passes through the point (2,7).
b) Graph the function
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

Quadratic Functions
Graph the following function using transformations:
f ( x)  2 x 2  6 x  2
Determine the domain and range of the function without using
a calculator.
Graph the following function by finding the vertex, axis of
symmetry, and y-intercept:
f ( x)  4 x 2  2 x  1
Determine the domain and range of the function without using
a calculator
3.1 Quadratic
Functions
Homework #25:
pgs. 164 – 166
#23 – 29 odd, 45 – 51 odd,
55, 57, 78, 79