Quadratic Functions

1
Quadratic Functions

• Section 2.2

2
Objectives

• Rewrite a quadratic function in vertex form using
  completing the square.
• Find the vertex of a quadratic function.
• Find x-intercepts and y-intercepts of a quadratic
  function.
• Write a quadratic function given two points.

3
Objectives

• Solve a word problem involving a quadratic
  function.
• Determine how a function has been transformed
  given an equation or a graph.
• Given a description of a transformed function,
  write the equation of the new function.

4
Vocabulary

• quadratic function
• parabola
• standard form of a quadratic equation
• completing the square

5
Given the function below find the vertex,
x-intercepts, and y-intercepts
6
Find a function whose graph is a parabola with
vertex (-2, -9) and that passes through the point
(-1, -6).
7
The profit function for a computer company is
given bywhere x is the number of units produced
(in thousands) and the profit is in thousand of
dollars.
8
Determine how many (thousands of) units must be
produced to yield maximum profit.
9
Determine the maximum profit.
10
Determine how many units should be produced for a
profit of at least 40 thousand dollars.
11
The graph of the functioncan be obtained from
the graph of f(x) by what transformation?
12
Given after performing the following
transformations, write the equation of the new
transformed function

• reflect over the x-axis
• shift upward 48 units
• shift 85 units to the right