LINEAR & QUADRATIC GRAPHS

Slides:



Advertisements
Similar presentations
Parent Function Booklet: Linear, Quadratic, Cubic, Absolute Value
Advertisements

Identify Linear, Quadratic, and Exponential Functions N Distinguish quadratic and exponential functions as nonlinear using a graph and/or a table.
Linear, Exponential, and Quadratic Functions. Write an equation for the following sequences.
Solving quadratic equations Factorisation Type 1: No constant term Solve x 2 – 6x = 0 x (x – 6) = 0 x = 0 or x – 6 = 0 Solutions: x = 0 or x = 6 Graph.
EXAMPLE 4 Find the zeros of a quadratic function Find the zeros of f(x) = x 2 + 6x – 7. SOLUTION Graph the function f(x) = x 2 + 6x –7. The x- intercepts.
Graphic Function
A Review of Graphing Functions. Cartesian Plane (2,5) (-4,3) (-7,-7) (1,-3)
10.1 Graphing Quadratic Functions p. 17. Quadratic Functions Definition: a function described by an equation of the form f(x) = ax 2 + bx + c, where a.
1.3 Families of Equations. What families of graphs have your studied? Linear Absolute Value Quadratic Square Root Cubic Cube Root.
October 3, 2012 Parent Functions Warm-up: How do you write a linear function, f for which f(1) = 3 and f(4) = 0? *Hint: y = mx + b HW 1.6: Pg. 71 #1-5,
Product and Quotients of Functions Sum Difference Product Quotient are functions that exist and are defined over a domain. Why are there restrictions on.
 Graph is a parabola.  Either has a minimum or maximum point.  That point is called a vertex.  Use transformations of previous section on x 2 and -x.
FUNCTIONS Relation – a set of ( x, y ) points Function – a set of ( x, y ) points where there is only one output for each specific input – x can not be.
EXAMPLE 5 Find the zeros of quadratic functions. Find the zeros of the function by rewriting the function in intercept form. a. y = x 2 – x – 12 b. y =
REVIEW FOR QUIZ 3 ALGEBRA II. QUESTION 1 FACTOR THE FOLLOWING QUADRATIC 3N 2 + 7N + 4 Answer: (3n + 4)(n + 1)
Objective: Students will be able to graph rational functions using their asymptotes and zeros.
FTCE 5-9 Test Prep Center for Teaching and Learning.
Aims: To be able to find the inverse of a function. To know the graphical relationship between a function and its inverse. To understand the relationship.
Mathematics 2 Unit 1 Mathematics 2 EOCT Review: Unit 1 The Great Quadratic.
5-1 Graphing Quadratic Functions Algebra II CP. Vocabulary Quadratic function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex.
Functions LINEAR AND NON LINEAR. Linear function What is the function that states that the range values are 2 more than the domain values?  f(x) = x.
Parent Functions. Learning Goal I will be able to recognize parent functions, graphs, and their characteristics.
Quadratics Review – Intercept & Standard Form August 30, 2016.
Use a graphing calculator to graph the following functions
Sketching the Derivative
Chapter 7 Functions and Graphs.
Chapter 4: Graphing Linear Equations
4.8 Modeling Real-World Data with Polynomial Functions
Comparing Linear, Exponential, and Quadratic Functions
We can use an equation, graph or table
Linear Equations Y X y = x + 2 X Y Y = 0 Y =1 Y = 2 Y = 3 Y = (0) + 2 Y = 2 1 Y = (1) + 2 Y = 3 2 Y = (2) + 2 Y = 4 X.
Use back - substitution to solve the triangular system. {image}
5.6 – The Quadratic Formula And Ch 5 Review
Points of intersection of linear graphs an quadratic graphs
Topics: Be able to writes equations of Linear Functions from numerical representations. Be able to writes equations of Absolute Value Functions from numerical.
mr-mathematics.com Recapping: Properties of quadratic graphs
Quadratics Review – Intercept & Standard Form
The graph of f(x) is depicted on the left. At x=0.5,
Algebra 150 Unit: Functions Lesson Plan #9: Function Tables and Graphing Objective SWBT plot a function from a function table.
Graph of the derived function
The Factor Theorem A polynomial f(x) has a factor (x − k) if and only if f(k) = 0.
Name:______________________________
Drawing Quadratic Graphs
Solving simultaneous linear and quadratic equations
2-4: Writing Linear Equations Using Slope Intercept Form
Algebra 1 Mini Posters Systems of Linear and Quadratic Equations
(4)² 16 3(5) – 2 = 13 3(4) – (1)² 12 – ● (3) – 2 9 – 2 = 7
Piecewise-Defined Function
Algebra 1 Section 6.3.
Solving Linear Equations by Graphing
Horizontal shift right 2 units Vertical shift up 1 unit
Horizontal Shift left 4 units Vertical Shift down 2 units
Drawing Graphs The parabola x Example y
“Yesterday was a good day……” Journey 1979
The Quadratic Curve Wednesday, 01 May 2019.
INEQUALITIES Many Kinds of Inequalities : Linear Inequalities
Quadratic Graphs.
Quadratic graphs.
Drawing other standard graphs
Graphing with X- and Y-Intercepts
Chapter 5: Graphs & Functions
Section 6.6 Day 1 Solving Systems of Inequalities
Solve each quadratic using whatever method you choose!
Graphing Quadratic Functions
5 Minute Check 1-4 Graph the equation : 2x + y – 4 = 0
Solving Quadratic Equations by Graphing
Unit 1 Jeopardy Review!.
The Quadratic Curve Monday, 27 May 2019.
Writing Rules for Linear Functions Pages
Line Graphs.
Presentation transcript:

LINEAR & QUADRATIC GRAPHS Functions & Graphs LINEAR & QUADRATIC GRAPHS

Graph the function f: x  2x + 1 for –1  x  5 -1 1 2 3 4 5 2X -2 6 8 10 Y 7 9 11

f(x) = 2x + 1 Now match up your x and y values (-1, -1 ) ( 0, 1 ) ( 0, 1 ) ( 1 , 3 ) ( 2 , 5 ) ( 3 , 7 ) ( 4 , 9 ) ( 5 , 11 )

Draw the graph of the function f(x) = x2 + x – 6 - 4  x  3 Quadratic Graphs Draw the graph of the function f(x) = x2 + x – 6 - 4  x  3 X -4 -3 -2 -1 1 2 3 X 2 16 9 4 - 4 - 6 -6 Y 6

For what values of x does f (x) = 0 -3 2 For what values of x does f (x) = 0 For f(x) = 0 x = - 3 or x = 2

Find the values of x when f(x) = 4 -3.7 2.7 Find the values of x when f(x) = 4 For f(x) = 4 x = - 3.7 or 2.7

Draw the graph of the function f(x) = - 2x2 + 7x – 3 -1  x  4 1 2 3 4 -2x2 -2 -8 -18 -32 7x -7 7 14 21 28 -3 y -12

Use your graph to find the value of f(2½) x = 2½ f(2½) = 2

f(x) = 0 0.5 3 Use your graph to find the values of x when f(x) = 0 x = 0.5 & x = 3

3.5 f(x) = - 3 Use your graph to find the value of x when f(x) = -3 x = 0 or 3.5