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Quadratic Functions

- Section 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.

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.

Vocabulary

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

Given the function below find the vertex,

x-intercepts, and y-intercepts

Find a function whose graph is a parabola with

vertex (-2, -9) and that passes through the point

(-1, -6).

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.

Determine how many (thousands of) units must be

produced to yield maximum profit.

Determine the maximum profit.

Determine how many units should be produced for a

profit of at least 40 thousand dollars.

The graph of the functioncan be obtained from

the graph of f(x) by what transformation?

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

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