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Warm-Up Explain how you made each match (Without a calculator!)
Section P.1: Graphs and Models p
4 Approaches to Mathematics: 1. Verbal – Explain in words 2. Numerical – Table of values 3. Graphical – Using graphs 4. Analytical – Manipulating symbols and equations
Sketch a graph of f(x) = 1 – x 2 Method 1: Make a table and plot points.
Sketch a graph of f(x) = 1 – x 2 Method 2: Using a graphing calculator.
Why not just always use a graphing calculator? Give the number of zeros of f(x) = sin(ln x)
Why not always just use a graphing calculator? Graph y =
Finding x and y-intercepts: x 2 y – x 2 + 4y = 0
Finding x and y-intercepts: y =
Symmetry: X-axis: Y-axis: Origin:
Check for symmetry: y = (x + 2) 2
Why does symmetry help? x – y 2 = 2
Find Points of Intersection and check: x 2 + y = 5 x – y = 1
P.1 Graphs and Models I’m so to be in Calculus!!!.
Test an Equation for Symmetry Graph Key Equations Section 1.2.
P.1 Graphs and Models Main Ideas Sketch the graph of an equation. find the intercepts of a graph. Test a graph for symmetry with respect to an axis and.
Notes Over 1.1 Checking for Symmetry Check for symmetry with respect to both axis and the origin. To check for y-axis symmetry replace x with x. Sym.
X and Y Intercepts. The y intercept is the point at which the graph of an equation crosses the y axis. y (0,3)(0,3) x y = 2x + 3.
1 To find the x-intercepts of y = f (x), set y = 0 and solve for x. INTERCEPTS AND ZEROS To find the y-intercepts of y = f (x), set x = 0; the y-intercept.
Warm Up… Solve each equation for y. (1)y – 5 = 4x (2) y + 2x = 7 (3) 2y + 6 = -8x Calculate the slope given the two points. (4) (-4, 4) and (2, -5) (5)
WARM - UP 1.Given the following information sketch a graph of the polynomial: 2.Find all of the roots of the following polynomial:
The Modulus Function Objectives: Understand what an absolute value is. Solve equations and inequalities involving modulus. Graph modulus functions.
P.1 Graphs and Models. Objectives Sketch the graph of an equation. Find the intercepts of a graph. Test a graph for symmetry with respect to an.
Section 4.1: Vertex Form LEARNING TARGET: I WILL GRAPH A PARABOLA USING VERTEX FORM.
Further Mathematics Workshop Stowupland High School 8 th November 2005 See next slide for details of how the lesson on curve sketching was organised.
Graphs of Quadratic Functions Graph the function. Compare the graph with the graph of Example 1.
Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry.
Section 1.2 Graphs of Equations in Two Variables.
Graphing Equations Slope Intercept form and Point Slope form.
LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You.
Meet the Parents Interception Who’s Line is It anyway?
1.2 Graphs of Equations. Objective Sketch graphs of equations Find x and y intercepts of graphs of equations Use symmetry to sketch graphs of equations.
Graphs & Models (P1) September 5th, I. The Graph of an Equation Ex. 1: Sketch the graph of y = (x - 1)
Bell Ringer. ASYMPTOTES AND GRAPHING December 2, 2015.
10.3 Solving Quadratic Equations – Solving Quadratic Eq. Goals / “I can…” Solve quadratic equations by graphing Solve quadratic equations using.
P7 The Cartesian Plane. Quick review of graphing, axes, quadrants, origin, point plotting.
Algebra 1B Chapter 9 Solving Quadratic Equations By Graphing.
Section 1.1 GRAPHS OF EQUATIONS. List the graphs that you are able to draw: Linear functions Quadratic functions Rational functions Radical functions.
Graphing Polar Graphs Calc AB- Section10.6A. Symmetry Tests for Polar Graphs 1.Symmetry about the x -axis: If the point lies on the graph, the point ________.
Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely.
Quadratic Graph Drawing. y = 4x 2 – 8x – 5 x y x y -1/23/2 -3 y = 4x 2 – 4x – 3.
Graph: x + y = 5 1. Solve for y. 2. Make an X|Y chart. 3. Graph.
MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions. b. Investigate and explain characteristics.
SOLUTION STEP 1 Use intercepts to graph an equation EXAMPLE 2 Graph the equation x + 2y = 4. x + 2y = 4 x = x- intercept 4 Find the intercepts. x + 2(0)
X AND Y INTERCEPTS. INTERCEPT In a function, an intercept is the point at which the graph of the line crosses an axis. If it crosses the y-axis it.
Entrance Slip: Quadratics 1)2) 3)4) 5)6) Complete the Square 7)
Determine if the following point is on the graph of the equation. 2x – y = 6; (2, 3) Step 1: Plug the given points into the given equation. 2(2) – (3)
Creating and Graphing Equations Using the x - intercepts Adapted from Walch Education.
Quadratic and Trig Graphs Learning Outcomes Revise solution of quadratic equation. Make tables of quadratic functions in order to make graphs. Investigate.
Warm Up 0?1? 2? Graph the linear functions.0?1? 2?
Polynomial Inequalities in One Variable Let P(x) be any polynomial. Then P(x) 0 are called polynomial inequalities. To solve polynomial inequalities: Use.
WARM UP 1. Explain how to graph a linear equation written in slope-intercept form. 2. Explain how to graph a linear equation written in point-slope form.
Find the zeros of a quadratic function from its graph. Find the axis of symmetry and the vertex of a parabola. Objectives.
Y – Intercept of a Line The y – intercept of a line is the point where the line intersects or “cuts through” the y – axis.
What is Calculus? Calculus is the mathematics of change: Velocity and Acceleration. Calculus is also the mathematics of tangent lines, slopes, areas,
Equations of Straight Line Graphs. Graphs parallel to the y -axis All graphs of the form x = c, where c is any number, will be parallel to the y -axis.
Graphs of Equations Objectives: Be able to find solutions, intercepts and the symmetry of a graph by hand and by using the calculator. TS: Analyzing.
Graphing Rational Functions Objective: To graph rational functions without a calculator.
WARM-UP: Graphing Using a Table x y = 3x 2 y -2 y = 3(-2) 2 -8 y = 3(-1) y = 3(0) y = 3(1) y = 3(2) 2 4 GRAPH. y = 3x
Chapter 3 – Linear Systems. Solving Systems Using Tables and Graphs Section 3.1.
Graphs of Functions Defined by Expressions in a Linear Equation On a standard screen, graph the following functions, determined from the given linear equation:
Review 2-1 and 2-2. Quiz Overview (non-calculator) 2-1a) graph power functions (4 points, 8 matching) b) solve radical equations (4 points, 2 equations)
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