STARTERTUE, OCT 7, 2014 These are ALL the same function written in different forms: (A) f(x) = (x + 4)(x – 2) (B) f(x) = (x + 1) 2 – 9 (C) f(x) = x 2 + 2x – 8 1.Which one is written in Standard Form? 2.Which one is written in Vertex Form? 3.Which on is written in Factored (Intercept) Form? 4.Use ANY form to find the following: a.Extrema b.Vertex c.Line of Symmetry d.X-Intercepts e.Y-Intercepts 5.How can you show that they are all in fact the same function? : Interpreting Key Features of Quadratic Functions

LATE WORK! You start out each quarter with three late passes. Once your late passes have been used, you cannot receive points if an assignment is turned in late. Absent If you were absent when the assignment was due, turn it in the next class period If you were absent when the assignment was given, you have 5 days to get it turned in When all else fails…look at the comments box in Skyward If the assignment is not turned in by that date, it is late and needs a late pass Not Absent If you do not have an assignment ready to correct when we correct it in class, it is late and needs a late pass. Next Quarter If you turn an assignment that needs a late pass and you do not attach a late pass, you will not be given the points. The assignment will be given back to you. If this happens on the deadline for that unit, you will not have the opportunity to turn it in again with a pass attached. You will get three new late passes for quarter : Interpreting Key Features of Quadratic Functions

Key Concepts The key features of a quadratic function are distinguishing characteristics used to describe, draw, and compare quadratic functions. Key features include the x-intercepts, y-intercept, minimums and maximums, and vertext Key features also include where the function is increasing and decreasing, where the function is positive and negative, symmetries, and the end behavior of the function : Interpreting Key Features of Quadratic Functions

Key Concepts, continued Increasing refers to the interval of x-values as the y-values are increasing. Decreasing refers to the interval of x-values as the y-values are decreasing. If a function is neither increasing nor decreasing it is said to be constant. Constant refers to the interval of x-values as the y-values are constant. Read the graph from left to right to determine when the function is increasing, decreasing, or constant : Interpreting Key Features of Quadratic Functions

Key Concepts, continued The concavity of a parabola is the property of being arched upward or downward. A quadratic with positive concavity (concave up) has a minimum where the vertex is the lowest point of the curve. (A smiley!) A quadratic with negative concavity (concave down) has a maximum where the vertex is the highest points of the curve. (A frowny!) : Interpreting Key Features of Quadratic Functions

Key Concepts, continued : Interpreting Key Features of Quadratic Functions Decreasing then Increasing Vertex: (0, –4) Minimum Graph decreases, then increases. Concave UP

Key Concepts, continued : Interpreting Key Features of Quadratic Functions Increasing then Decreasing Vertex: (0, 4) Maximum Graph Increases, then decreases. Concave Down

Key Concepts, continued : Interpreting Key Features of Quadratic Functions End Behavior of a Smiley

Key Concepts, continued : Interpreting Key Features of Quadratic Functions End Behavior of a Frowny

Key Concepts, continued Functions can be defined as odd or even based on the output yielded when evaluating the function for –x. For an odd function, f(–x) = –f(x). That is, if you evaluate a function for –x, the resulting function is the opposite of the original function. For an even function, f(–x) = f(x). That is, if you evaluate a function for –x, the resulting function is the same as the original function : Interpreting Key Features of Quadratic Functions

: Interpreting Key Features of Quadratic Functions Key Concepts, continued EVEN functions are symmetric to the y-axis ODD functions are symmetric to the origin. If a function is neither ODD nor EVEN it is said to be NEITHER. Quadratics (Parabolas) can only be EVEN or NEITHER. What kind of parabolas are symmetric to the y-axis? What kind of parabolas are not symmetric to the y-axis?

: Interpreting Key Features of Quadratic Functions Analyzing Graphs of Functions Increasing and Decreasing

: Interpreting Key Features of Quadratic Functions Analyzing Graphs of Functions Positive and Negative

: Interpreting Key Features of Quadratic Functions Analyzing Graphs of Functions End Behavior, Even/Odd/Neither, Concavity

Guided Practice Example 1 A local store’s monthly revenue from T-shirt sales is modeled by the function f(x) = –5x x – 7. Use the equation and the graph on the next slide to answer the following questions: At what prices is the revenue increasing? Decreasing? What is the maximum revenue? What prices yield no revenue? Is the function even, odd, or neither? : Interpreting Key Features of Quadratic Functions

Guided Practice: Example 1, continued : Interpreting Key Features of Quadratic Functions *At what prices is the revenue increasing? Decreasing? *What is the maximum revenue? *What prices yield no revenue? *Is the function even, odd, or neither? f(x) = –5x x – 7

Guided Practice Example 2 A function has a minimum value of –5 and x-intercepts of –8 and 4. What is the value of x that minimizes the function? For what values of x is the function increasing? Decreasing? : Interpreting Key Features of Quadratic Functions