Ch 2 – Polynomial and Rational Functions

2.1 – Quadratic Functions

Definition of a Quadratic Function

• Let a, b, and c be real numbers with a ≠ 0. The function f(x) = ax2 + bx + c is called a quadratic function.

Vocabulary

• Parabola – the graph of a quadratic function

• Vertex – the maximum/minimum of a parabola

• Axis of Symmetry – the line in which the parabola is symmetric. It passes through the vertex.

Vertex Form

• f(x) = a(x – h)2 + k, a ≠ 0.

• (h, k) is the vertex• x = h is the axis of symmetry• a > 0, the parabola opens up• a < 0, the parabola opens down

Use the function, f(x) = -x2 + 6x – 8 to answer the following

questions.1. Describe the graph.2. Identify the vertex and axis of symmetry.3. Identify any x-intercepts.

Find the vertex form of the equation of a parabola that has a vertex at (1, 2)

and passes through (3, -6)

Write an equation of a quadratic function that has a vertex at (-2, -2)

and passes through the (-1, 0)

Business A manufacturer of lightning fixtures has daily production costs of C = 800 – 10x + 0.25x2 where C is the total cost (in dollars) and x is the number of units produced. How many fixtures should be produced each day to yield a minimum cost?

Vertical Free Fall Model

• The height, s, and vertical velocity, v, of an object in free fall is

• t is time in seconds, g ≈ 32 ft/sec2 ≈ 9.8 m/sec2, v0 is initial velocity, s0 is initial height

Free Fall Model As a promotion for the Houston Astros, a competition is held to see who can throw a baseball the highest from the front row of the upper deck of seats, 83 ft above field level. The winner throws the ball with an initial vertical velocity of 92 ft/sec2 and it land on the infield grass. a) Find the maximum height of the base ball.b) How much time is the ball in the air?