By Katie McKnight & Peter Myszka. This is our beginning equation. It is a quadratic function that will give us a good base to examine the equation of.

Slides:

Advertisements

Similar presentations

Learning Log # The Limit of a Function Uses of the word Limit in everyday life (speed) Roughly speaking, the Limit is the y-value that the function.

Advertisements

Warm Up… Solve each equation for y.

Equations of Tangent Lines

Equations of Tangent Lines

Find the slope of the tangent line to the graph of f at the point ( - 1, 10 ). f ( x ) = 6 - 4x

Derivatives - Equation of the Tangent Line Now that we can find the slope of the tangent line of a function at a given point, we need to find the equation.

Calculating Slope of a Line :

Graph linear functions EXAMPLE 1 Graph the equation. Compare the graph with the graph of y = x. a.a. y = 2x b.b. y = x + 3 SOLUTION a.a. The graphs of.

Graphing Using Slope - Intercept STEPS : 1. Equation must be in y = mx + b form 2. Plot your y – intercept ( 0, y ) 3. Using your y – intercept as a starting.

Graphing Linear & Quadratic Equations Brought to you by Tutorial Services – The Math Center.

Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.

The slope-intercept form of a linear equation of a non-vertical line is given by: Slope-Intercept Form of a Linear Equation.

Solving Systems of Equations Graphically. Quadratic Equations/ Linear Equations  A quadratic equation is defined as an equation in which one or more.

Numerical Derivative l MATH l (8:) nDeriv( MATH. Numerical Derivative l MATH l (8:) nDeriv( l nDeriv(f(x),x,a) gives f ’ (a) l Try f(x)=x^3 at x=2, compare.

Find the x and y intercepts of each graph. Then write the equation of the line. x-intercept: y-intercept: Slope: Equation:

3.1 The Derivative Tues Sept 22 If f(x) = 2x^2 - 3, find the slope between the x values of 1 and 4.

Odd one out Can you give a reason for which one you think is the odd one out in each row? You need to give a reason for your answer. A: y = 2x + 2B: y.

+ Day 17: Direct Variation What is a constant of variation?

Find the slope of the line through P(-6,2) and Q(-5,3) m.

Chapter 6 Test Prep 6-3 through 6-5: Solving Quadratic Equations 6-6: Graphing Quadratic Functions Application Problems Choose a section to work on. At.

The Graphs of Quadratic Equations A quadratic equation is an equation that has a x 2 value. All of these are quadratics: y = x 2 y = x y = x 2 +

Some needed trig identities: Trig Derivatives Graph y 1 = sin x and y 2 = nderiv (sin x) What do you notice?

OBJECTIVE: USE THE SLOPE INTERCEPT FORM TO GRAPH A LINE Slope Intercept Form.

Graphing Equations Slope Intercept form and Point Slope form.

Solving Quadratic Equations By: Jessica Campos. Solving Quadratic Equations by Graphing F(x)= x 2 -8x+15=0 X=(x-3)(x-5) X=3 and 5 Steps to put into a.

Quadratic Equation (Standard Form) Quadratic Term Linear Term Constant Term 5.1 Graphing Quadratic Function, p. 249 Objective: To Graph Quadratic Functions.

COMPASS Test Model Help What is the sum of the solutions of the equation  A. 8  B.-8  C. 2  D.-2  E. 15 Go on Calculator.

Unit 3 Section : Regression Lines on the TI  Step 1: Enter the scatter plot data into L1 and L2  Step 2 : Plot your scatter plot  Remember.

More with Rules for Differentiation Warm-Up: Find the derivative of f(x) = 3x 2 – 4x 4 +1.

Zooming In. Objectives  To define the slope of a function at a point by zooming in on that point.  To see examples where the slope is not defined. 

Linear Graphs and Modelling Plotting straight line graphs Plotting linear graphs on the calculator Finding gradients of straight lines Equations of straight.

Graphing Linear Equations

Integrated Mathematics. Objectives The student will be able to:: 1. graph linear equations. 2. write equations in point- slope form.

Recall that the slope-intercept form of a linear equation of a non-vertical line is given by: Graphing Using Slope-Intercept Form.

First choose an equation. Next graph it Then you choose the best fitting window.

SLOPE-INTERCEPT FORM Book Sections 4.1/4.2 Essential Question: How can we write and graph equations when using slope- intercept form?

Equation for a Vertical Line and a Horizontal Line

F-IF.C.7a: Graphing a Line using Slope-Intercept, Part 2

2. Derivatives on the calculator

Chapter 7 Functions and Graphs.

Use a graphing calculator to determine the graph of the equation {image} {applet}

Equations of straight lines

Any two equations for the same line are equivalent.

Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

Solving Quadratic Equations using the Quadratic Formula

Slope Intercept Form Lesson 6-2.

Section 2-4: Writing Linear Equations

A graphing calculator is required for some problems or parts of problems 2000.

Quadratic Equations L.O.

y x y = x + 2 y = x + 4 y = x – 1 y = -x – 3 y = 2x y = ½x y = 3x + 1

5.6 – point slope formula Textbook pg. 315 Objective:

Write the equation for the following slope and y-intercept:

8-6 Slope-Intercept Form

Objective: To know the equations of simple straight lines.

Distance Time Graphs.

Slope-intercept Form of Equations of Straight Lines

Warm Up # 3 Complete POST – Assessment INDIVIDUALLY!!!!

Quadratic Graphs.

Drawing other standard graphs

Graphs of Functions.

Solve each quadratic using whatever method you choose!

Objectives: To graph lines using the slope-intercept equation

Draw Scatter Plots and Best-Fitting Lines

More with Rules for Differentiation

Which of the following expressions is the equation of the function {image} {applet}

1: Slope from Equations Y = 8x – 4 B) y = 6 – 7x

Section 2-4: Writing Linear Equations

Graphing using Slope-Intercept Form

Objective: To know the equations of simple straight lines.

Presentation transcript:

By Katie McKnight & Peter Myszka

This is our beginning equation. It is a quadratic function that will give us a good base to examine the equation of slopes.

This is the window we used for the equation, and how the equation looks. From this point, we found the slope value for 5 certain points to see a basic image of the slopes.

These are the five points we choose randomly. Next to it is a screen shot of the function and a plot of those points. You can already see, that for a quadratic function the slope line is a straight line.

We had the calculator do the nDeriv command, which calculates the slopes line. Then we found the equation of the slopes line, and graphed it on the calculator. The two functions were the same.

All this leads up to the conclusion, that the derivative always is the equation of the slopes, for every function. So next time the only command you have to know for the slopes, is the Derivative.