Topics:

• Standard and Vertex form of a Quadratic Function

• Finding Key Features of a Quadratic algebraically and graphically.

• Graphing Quadratics

*MAT 150 – AlgebraClass #8

*Standard Form of a Quadratic Equation

Several key features can be determined from the standard form:

*Concavity

*Vertex (minimum or maximum)

*Axis of Symmetry

*y-intercepts

*X-intercepts

*ALL QUADRATICS ARE A PARABOLA!

Determining Concavity

Function Is it Quadratic?(circle one)

If Quadratic, what is the Concavity?

(circle one)

Yes No Up Down

Yes No Up Down

Yes No Up Down

Yes No Up Down

If a > 0, the parabola is concave up. If a < 0, the parabola is concave down.

Finding the Vertex (min/max)

Function Vertex(show work)

Maximum or Minimum?(circle one)

Max Min

Max Min

Max Min

𝒙=−𝒃𝟐𝒂

Vertex Form of a Quadratic

Function VertexMaximum or Minimum?(circle one)

Max Min

Max Min

Max Min

Using the Vertex in a Real-Life Situation

Suppose the monthly revenue from the sale of Carlson 42-inch 3D televisions is given by the function dollars, where x is the number of televisions sold.

a) How many televisions must be sold to make a maximum amount of revenue?

b) What is the maximum amount of revenue to be made?

c) For how many televisions would the monthly revenue be increasing?

Graphing Quadratic Functions

Steps

1. Find the vertex

2. Make a table of values centered around the vertex. (At least 5 points)

3. Graph on a coordinate plane.

Graph the following:

Finding x- and y-intercepts graphically

FunctionX-intercept(s)

2nd, TRACE, #2

Y-intercept

TRACE, 0, ENTER

Putting it all together

A ball is thrown upward at 64 ft per second from the top of an 80-foot-high building given by the function .

A. How high does the ball go?

B. How long did it take to reach the maximum height?

C. When will the ball hit the ground?

D. How high is the ball when it is first thrown?

E. How long will it take the ball to reach a height of 130ft?

Assignment

Pg. 178-182

#1-4 all

#21-24 all

#57-63 all