QUADRATICS: finding vertex

Slides:

Advertisements

Similar presentations

Ch. 6.1: Solve Quadratic Equations by Graphing

Advertisements

Quadratic graphs Today we will be able to construct graphs of quadratic equations that model real life problems.

Modeling with Quadratic Functions IB Math SL1 - Santowski.

Warm-Up: December 15, 2011  Divide and express the result in standard form.

Quadratic and Exponential Functions

Graph the quadratic function using a table with 5 points. Write the vertex, axis of symmetry, y- intercept, is vertex a minimum or maximum.

Essential Question: How do you find the vertex of a quadratic function?

Back to last slideMain Menu Graphing, Max/Min, and Solving By Mrs. Sexton Calculator Tips.

Maybe we should look at some diagrams.

Quadratic Graphs – Day 2 Warm-Up:

1.8 QUADRATIC FUNCTIONS A function f defined by a quadratic equation of the form y = ax 2 + bx + c or f(x) = ax 2 + bx + c where c  0, is a quadratic.

Warm-up Problems Match each situations with one of the following graphs. 1. A company releases a product without advertisement, and the profit drops. Then.

5.1: Graphing Quadratic Functions

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–1) CCSS Then/Now New Vocabulary Example 1:Two Real Solutions Key Concept: Solutions of a Quadratic.

Section 3.1 Quadratic Functions; Parabolas Copyright ©2013 Pearson Education, Inc.

EOC PREP Session B. Identify a.) the vertex b.) the axis of symmetry and c.) both the x and y intercepts of each quadratic function. A B.

Jeopardy Factoring Quadratic Functions Zeroes and Vertex Describing Polynomials Modeling & Regression Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200.

4.1 and 4.7 Graphing Quadratic Functions. Quadratic function a function that has the form y = ax 2 + bx + c, where a cannot = 0.

4-2 Quadratic Functions: Standard Form Today’s Objective: I can graph a quadratic function in standard form.

Quadratic Equations in the Real World Keystrokes: At the bottom of the display are the coordinates of the maximum point on the graph. The y-value of these.

1. Use the discriminant to determine the number and type of roots of: a. 2x 2 - 6x + 16 = 0b. x 2 – 7x + 8 = 0 2. Solve using the quadratic formula: -3x.

Today in Algebra 2 Go over homework Need a graphing calculator. More on Graphing Quadratic Equations Homework.

GRAPH THE FOLLOWING FUNCTION (WITHOUT A CALCULATOR). 1) y = 3 x 2 – 2 x – 1 1) Find the vertex. y = 3( 1 / 3 ) 2 – 2( 1 / 3 ) – 1 y = - 4 / 3 V = ( 1.

4.1 – 4.3 Review. Sketch a graph of the quadratic. y = -(x + 3) Find: Vertex (-3, 5) Axis of symmetry x = -3 y - intercept (0, -4) x - intercepts.

Graphing Calculator Steps Steps to follow to find the vertex of a parabola & to find the zeros of a parabola. Make sure you view this in presentation mode.

For f(x) = x 2 – 3x – 15 find f(-2) -5. x y Vertex: (0, 3) Axis of symmetry: x = 0 Determine the vertex, axis of symmetry and graph.

Unit 2: Quadratic Functions

Quadratic Word Problems. Sketch a graph The path of a baseball is given by the function where f(x) is the height of the baseball in feet and x is the.

Solving Story Problems with Quadratic Equations. Cost and Revenue Problems The cost in millions of dollars for a company to manufacture x thousand automobiles.

Warm Up Lesson 4.1 Find the x-intercept and y-intercept

Section 2.2 Quadratic Functions. Graphs of Quadratic Functions.

Quadratic Applications Special Topics: Fall 2015.

Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing  DESCRIBE the Elements of the GRAPH of a Quadratic Equation  DETERMINE a Standard Approach.

Graphing quadratic functions part 2. X Y I y = 3x² - 6x + 2 You have to find the vertex before you can graph this function Use the formula -b 2a a = 3.

Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:

4.2 Standard Form of a Quadratic Function The standard form of a quadratic function is f(x) = ax² + bx + c, where a ≠ 0. For any quadratic function f(x)

Day 14: Quadratics Goal: To graph a quadratic function using the axis of symmetry, vertex and zeroes. Standard: – Sketch graphs of linear, quadratic.

Section 2.2 Quadratic Functions. Thursday Bellwork 4 What does a quadratic function look like? 4 Do you remember the standard form? 4 How could we use.

Chapter 4: Polynomials Quadratic Functions (Section 4.1)

MAT 150 Unit 2-1: Quadratic Functions; Parabolas.

Quadratic Functions; Parabolas Determining if a Function is Quadratic Highest exponent in the equation is 2, no more no less.

Given find the following a) Vertex b) Axis of Symmetry c) Y-intercept

UNIT 1: QUADRATICS Final Exam Review. TOPICS TO COVER  GCF  Factoring  Solving Quadratic Equations  Graphing Quadratic Equations  Projectile Motion.

Graphs Day 2. Warm-Up HW Check Complete the investigation: Pairs will display their work under the doc cam. Make sure your work is neat!!!

Section 4.1 Notes: Graphing Quadratic Functions

Warm Up x2 + 2x + 4 = 0 2x2 + 3x - 5 = 0 x2 - 2x + 8 = 0

Warm Up – copy the problem into your notes and solve. Show your work!!

4.1 Graphing Quadratic Functions

Write your estimate in your warm-up section.

Five-Minute Check (over Lesson 3–1) Mathematical Practices Then/Now

Parts of a Parabola and Vertex Form

* Graphing * Max/Min * solving

Solving Quadratic Equation by Graphing

Solving Equations Graphically

Unit 12 Review.

Graph y = -5x2 – 2x + 3 and find the following:

Quadratic Functions.

Homework Corrections (Page 1 of 2)

Graphing Calculator Lesson

Section 9.1 Day 2 Graphing Quadratic Functions

Algebra 2/Trigonometry Name: __________________________

Warm up Put each of the following in slope intercept form 6x + 3y = 12

Find the x-intercept and y-intercept

LEARNING GOALS - LESSON 5.3 – DAY 1

Unit 6 Review Day 1 – Day 2 Class Quiz

NO GRAPHING CALCULATORS.

Tutoring is on Tuesdays and Thursdays from 7:45 to 8:15 a.m.

Warmup Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -3x2 + 12x.

Presentation transcript:

QUADRATICS: finding vertex EOC TEST STRATEGIES: QUADRATICS: finding vertex

VErTEx KEY TERMS METHODs TO FIND “MAXIMUM” “MINIMUM” TURNING POINT” *Sometimes the problem may ask for the axis of symmetry. How does this connect with the vertex?

EXAMPLE 1.1- Using formula Suppose a company has daily production costs that are modeled by the function C(x) = 800 -10x + 0.25x2 where C is the total cost in dollars and x is the number of units produced. What is the minimum production cost?

EXAMPLE 1.1- Using calculator table FIRST – type equation in “Y=“ Then – go to “2ND” “TABLE” And page down to see the turning point. (20 unit, $700) Suppose a company has daily production costs that are modeled by the function C(x) = 800 -10x + 0.25x2 where C is the total cost in dollars and x is the number of units produced. What is the minimum production cost?

EXAMPLE 1.1- Using calculator trace Arrow left & “enter” Arrow right & “enter” “Enter” once more when it says ‘guess?’ Minimum FIRST – type equation in “Y=“ Then – “2nd” “Trace” next – choose #3 “minimum” “ENTER” (you will need to adjust the window)

OTHER THINGS TO NOTE underline the variables. READ the question. Identify the variable being asked for. Suppose a company has daily production costs that are modeled by the function C(x) = 800 -10x + 0.25x2 where C is the total cost in dollars and x is the number of units produced. What is the minimum production cost?

CHECK IT: Q#1.2 The amount of profit a company makes if they spend x dollars on advertising is modeled by the function P(x) = -5x2 + 400x + 1,200. How much should the company spend on advertising to maximize profit?

CHECK IT Q1.3 A ball is thrown into the air with a speed of 32 feet per second. The function h = 32t – 16t2 models the height of the ball after t seconds. What is the maximum height of the ball?

CHECK It q1.4 Suppose the equation h(t) = -t2 + 5t + 14 models the height of a ball thrown into the air off the top of the bleachers. How many seconds does it take for the ball to reach its maximum height?

Check it Q1.5 Penny creates produces Penny Blossoms in her apartment. The quadratic function, p(n) = -2n2 + 24n – 25, can be used to determine her weekly profit where n is the number of Penny Blossoms made. At what number of Penny Blossoms does the profit begin to decrease?

Check it q1.6 What is the axis of symmetry for the function f(x) = 4x2 + 2x + 1?