1. A person throws a baseball into the air with an initial vertical velocity of 30 feet per second and then lets the ball hits the ground. The ball is.

Slides:

Advertisements

Similar presentations

 Understand that the x-intercepts of a quadratic relation are the solutions to the quadratic equation  Factor a quadratic relation and find its x- intercepts,

Advertisements

Module 2 Quadratic Functions

EXAMPLE 6 Write a quadratic function in vertex form Write y = x 2 – 10x + 22 in vertex form. Then identify the vertex. y = x 2 – 10x + 22 Write original.

LIAL HORNSBY SCHNEIDER

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

ACTIVITY 27: Quadratic Functions; (Section 3.5, pp ) Maxima and Minima.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 3 Polynomial and Rational Functions Copyright © 2013, 2009, 2005 Pearson Education, Inc.

Warm-up Problems Simplify Solve -2(x – 3)2 = 24

Chapter 8 Review Quadratic Functions.

Graphs of Quadratic Functions Any quadratic function can be expressed in the form Where a, b, c are real numbers and the graph of any quadratic function.

Definition of a Polynomial Function in x of degree n.

Section 6 Part 1 Chapter 9. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives More About Parabolas and Their Applications Find.

Over Chapter 8 A.A B.B C.C D.D 5-Minute Check 2 (2z – 1)(3z + 1) Factor 6z 2 – z – 1, if possible.

Chapter 5 Quadratic Functions Review. Question 1a Identify the vertex, the axis of symmetry, create a table, then graph. y = x² - 8x + 5.

MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations.

Math Jeopardy Quad. Functions And Square Roots Graphing Quad. Equations Solving Quad. Equations Vertical Motion “Algebra – Chapter 9” Critical Values.

9-4 Quadratic Equations and Projectiles

3.1 Quadratic Functions. Polynomials- classified by degree (highest exponent) Degree: 0 -constant function-horizontal line 1 -linear function- 2 -quadratic.

10.6 Plane Curves and Parametric Equations. Let x = f(t) and y = g(t), where f and g are two functions whose common domain is some interval I. The collection.

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.

Quarterly Assessment 3 Warm Up # 3 Work on your Make up QA.

Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.

SAT Problem of the day: The graph of a quadratic function y is shown. For what value of x does y attain its greatest value? y = – x 2 + 6x – 3 Applications.

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.

Roots, Zeroes, and Solutions For Quadratics Day 2.

$200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400.

Essential Question: How do you sketch graphs and write equations of parabolas? Students will write a summary of the steps they use toe sketch a graph and.

Aim: How do we apply the quadratic equation? Do Now: Given a equation: a) Find the coordinates of the turning point b) If y = 0, find the values of x.

Quadratic Solutions The number of real solutions is at most two. No solutionsOne solutionTwo solutions The solutions are located on the x axis, or the.

Solving Quadratics Roots and Vertices Forms Quadratic Formula Hodge- Podge Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final.

Section 1.3 Quadratic Equations 1. 2 OBJECTIVE 1 3.

Twenty Questions Algebra 2012 EOC Review Twenty Questions

CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.

 Given a quadratic equation in standard form, the value of x can be found by using the quadratic formula:

Lesson 9.5 Objective: To solve quadratic equations using the quadratic formula. Quadratic formula: When Then the value of x is… What formula can be used.

Factoring to Solve Quadratic Equations – Solving Quadratic Equations by Factoring A quadratic equation is written in the Standard Form, where a,

NOTES 0-5C QUADRATIC FORMULA Student Learning Goals: Students will be able to solve quadratic equations using the quadratic formula.

Factor each polynomial.

Quadratic Word Problems

Quadratic Functions, Quadratic Expressions, Quadratic Equations

HW: Worksheet Aim: How do we apply the quadratic equation?

Warm-Up Solve by factoring:

How can you derive a general formula for solving a quadratic equation?

Find the number of real solutions for x2 +8x

Module 4 Quadratic Functions and Equations

Notes Over 9.6 Quadratic Formula

ALGEBRA II HONORS/GIFTED SECTION 4-5 : QUADRATIC EQUATIONS

Math 2 Bell Ringers Day 1 – Day 90.

Algebra 5/5/14 Bell Ringer 5 Minutes

Quadratic Functions (Graphing)

Section 1.5 Quadratic Equations

Lesson 2.1 Quadratic Functions

Review Day M2 Unit 1C: Day 8.

Quadratic Function model

Solve by Graphing Solve by Factoring Complex Numbers Solve by

GSE Algebra I Unit 4/5/6 Review.

GSE Algebra I Unit 4/5/6 Review.

A quadratic equation is written in the Standard Form,

A quadratic equation is written in the Standard Form,

Notes Over 9.5 Quadratic Formula

Completing the Square. The Quadratic Formula.

A quadratic equation is written in the Standard Form,

Unit 6 Review Day 1 – Day 2 Class Quiz

Solve using factoring or square root property.

A quadratic equation is written in the Standard Form,

QUADRATIC FUNCTION PARABOLA.

Graphing Quadratic Functions

Solving Quadratics Algebraically

Presentation transcript:

1. A person throws a baseball into the air with an initial vertical velocity of 30 feet per second and then lets the ball hits the ground. The ball is released 5 feet above the ground. For how many seconds is the ball in the air? (Use the formula )

2. A city wants to increase the area of a rectangular playground that is 72 feet by 48 feet by adding the same distance x to the length and the width. The new area is to be no more than double the current size. Write and solve an equation to find the maximum value of x.

3. A football was kicked at the beginning of a game 3. A football was kicked at the beginning of a game. The “hang time” of the football was 3 seconds, and it reached a height of 36 feet. Write the quadratic equation in factored form that describes the path of the football.

4. Using the discriminant, determine the number and nature of the roots for each of the following quadratic equation. x2 – 8x + 14 = 0

5. Using the discriminant, determine the number and nature of the roots for each of the following quadratic equation. x2 – 8x + 16 = 0 -6 1

6. Find the missing length x+5

7. Given f(x) = 3x2 + 7x – 6, write f(x) in factored (-5,32)

8. Given the graph of f(x), write the equation of f(x) in: a. Factored form b. Vertex form 90

9. Given the inequality y > x2 + 7x + 12, which point is a solution 9. Given the inequality y > x2 + 7x + 12, which point is a solution. a. (-3, 0) b. (0, 12) c. (-2, 3) d. (-1,-1)

10. Given the graph, determine which of the following pairs of zeros could correspond. A. -4.76 and 1.76 B. -5.16 and 1.16 C. -2 and -10 D. -6.42 and 2.42 (1,0) (-3,0)

11. Solve the following equation. 0 = 2x2 + 6x + 12

Solve the following inequality.

13. Find the vertex of the following parabola: 2 real roots

14. You have an arched window 14. You have an arched window. You are modeling the arch on a coordinate plane. The bottom of the arch is at (-5,0) and (1,0). The arch is 27 units tall. Write the 3 forms of the Quadratic.

15. Write the equation of a parabola with a vertex of (-4, -8) and a y-intercept of 12.

16. Find the roots of a parabola: c

17. Mr. Jones is making a vegetable garden 17. Mr. Jones is making a vegetable garden. The area needed for each watermelon and its surrounding area is 450 square inches. Mr. Jones is planting them in a rectangular garden that the length is 20 inches less than 3 times its width. Mr. Jones planted 50 plants. What is the width? 1 real root

18. Find the area of the triangle whose base is and whose height is 2.03

19. Factor: B

20. Factor and solve:

KEY! 1>18>3>15>6>11>2>20>4>13 7>12>5>17>8>14>9>16>10>19>1