Homework Review Lesson 3.1B

Characteristics of Quadratics Unit 5a Day 2

Graphing a Quadratic Function EQ: How do we identify all of the important characteristics of a quadratic? Lesson 3.1B

Today, we are going to begin by reviewing what we have learned yesterday from graphing in vertex form. Lets recall how to find the following: Vertex Axis of Symmetry Maximum or Minimum Y-intercept

c) Since a > 0 , the parabola opens up and has a: minimum Find: a) vertex b)axis of symmetry c) state whether the vertex is a maximum or minimum. d) y-intercept Shifted up 2 units a) Vertex: (0, 2) b) Axis of symmetry: x = 0 c) Since a > 0 , the parabola opens up and has a: minimum d) y-intercept: (0, 2) 5

Reflected about x-axis Left 2 units Up 4 units Find: a) vertex b) axis of symmetry c) state whether the graph has a maximum or minimum. d) y - intercept Reflected about x-axis Left 2 units Up 4 units a) Vertex: (-2, 4) b) Axis of symmetry: x = -2 c) Since a < 0 , the parabola opens down and has a: maximum d) y-intercept: (0, 0) 6

Domain VS. Range Domain: (x – values) read domain from left to right Range: (y-values) read range from bottom to top

The DOMAIN of parabolas is all real numbers… unless the parabola looks like this and has endpoint(s) We say the domain is restricted, therefore it is no longer all real numbers 8

Find the domain of the graph below -1 < x < 2 9

Domain: -2 < x < 2 Range: 0 < y < 4 Find the domain and range of the graph below Domain: -2 < x < 2 Range: 0 < y < 4 10

Domain: -∞ < x < ∞ Range: -∞ < y < 4 Find the domain and range of the graph below Domain: -∞ < x < ∞ Range: -∞ < y < 4 11

Graph the quadratic using the axis of symmetry and vertex. Y-intercept: Max or Min? maximum Extrema: y = 3 Domain: Range: All real numbers y ≤ 3 12

Graph the quadratic using the axis of symmetry and vertex. (-1, 0) Axis of symmetry: Y-intercept: Max or Min? minimum Extrema: y = 0 Domain: Range: All real numbers y ≥ 0 13

What are these lines doing from left to right? Intervals of increase and decrease To determine the intervals of increase and decrease, you must “read” the graph from left to right What are these lines doing from left to right? 14

Let’s apply this idea to parabolas… To determine the intervals of increase and decrease, you must “read” the graph from LEFT to RIGHT What is this parabola doing on the left side of the vertex? What is this parabola doing on the right side of the vertex? Going downhill Going uphill Interval of decrease Interval of increase 15

One more… Going uphill Going downhill What is this parabola doing on the left side of the vertex? What is this parabola doing on the right side of the vertex? Going uphill Going downhill Interval of decrease Interval of increase 16

Graph each quadratic function and determine the interval of increase and decrease y = (x+1)²+2 Interval of decrease Interval of increase 17

Graph each quadratic function and determine the interval of increase and decrease Interval of decrease Interval of increase 18

Determine if the given interval is an interval of increase or decrease 19

Rate of Change To determine the rate of change, find the slope of the line that passes through two given points on the function. 20

Find the rate of change on the interval: -1≤x≤2 21

End Behavior The value a function, f(x), approaches when x is extremely large (∞) or when x is extremely small (-∞). 22

Even and Odd Functions

Assignment: Practice Worksheet 24