For example: f(x)=6x2+17x-14.

Slides:

Advertisements

Similar presentations

Warm Up For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward or downward. 1. y = x y.

Advertisements

MA.912.A.7.2: Solve quadratic equations by factoring and using the quadratic formula. f(x) = −x x − 21 The function below can be used to describe.

EXAMPLE 5 Solve a vertical motion problem Juggling

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

Day 4 What number inserted into the following expression would complete the square?

EXAMPLE 4 Solve a quadratic equation Solve 6(x – 4) 2 = 42. Round the solutions to the nearest hundredth. 6(x – 4) 2 = 42 Write original equation. (x –

9.2: QUADRATIC FUNCTIONS: Quadratic Function: A function that can be written in the form y = ax 2 +bx+c where a ≠ 0. Standard Form of a Quadratic: A function.

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.8 – Graphing and Solving Quadratic.

2-3: Solving Quadratic Equations by Factoring

Objectives Solve quadratic equations by graphing or factoring.

5-3 Solving Quadratic Equations by Graphing and Factoring Warm Up

Warm Up Set each function equal to zero, and then solve for the zeros

4.8 – Use the Quadratic Formula and the Discriminant

Section 10-7 & 8 Quadratic Formula and Discriminant SPI 23E: Find the solution to a quadratic equation given in standard form SPI 23H: select the discriminant.

5.6: The Quadratic Formula and the Discriminant Objectives: Students will be able to… Solve a quadratic equation using the quadratic formula Use the discriminant.

Example: 3x 2 + 9x + 6. Solving Quadratic Equations.

SECTION 3.4 POLYNOMIAL AND RATIONAL INEQUALITIES POLYNOMIAL AND RATIONAL INEQUALITIES.

3.3 Solve Quadratic Equations by Graphing & by Factoring

To find the x coordinate of the vertex, use the equation Then substitute the value of x back into the equation of the parabola and solve for y. You are.

SAT Problem of the Day.

Holt Algebra Solving Quadratic Equations by Graphing and Factoring Solve quadratic equations by factoring. Find roots of quadratic equations. Graph.

Chapter 2 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Polynomial and Rational Inequalities.

Lesson 9-8 Warm-Up.

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 =

SWBAT… solve quadratic equations in the form a x 2 + bx + c Tues, 5/14 Agenda 1. Warm-up (10 min) 2. Review HW#1 and HW#2 (20 min) 3. ax 2 + bx + c = 0.

10.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Solve Quadratic Equations by the Quadratic Formula.

Section 10.6 Solve Any Quadratic Equation by using the Quadratic Formula.

1.8 Quadratic Formula & Discriminant p. 58 How do you solve a quadratic equation if you cannot solve it by factoring, square roots or completing the square?

Bonus! Multiplying Binomials Factoring Solving By Factoring.

EXAMPLE 6 Solve a multi-step problem An athlete throws a shot put with an initial vertical velocity of 40 feet per second as shown. a. Write an equation.

EXAMPLE 5 Solve a vertical motion problem A juggler tosses a ball into the air. The ball leaves the juggler’s hand 4 feet above the ground and has an initial.

Warm-Up Exercises Evaluate the expression for the given value of x – (–x) + 9; x = – – x + 3; x = 8 ANSWER 22 ANSWER 9.

Warm-Up Exercises Find the zeros of the polynomial function. 1.f(x) = x 2 + 5x – 36 2.f(x) = x 2 – 9x + 20 ANSWER –9, 4 ANSWER 4, 5.

ALGEBRA 1 Lesson 9-7 Warm-Up. ALGEBRA 1 “Using the Quadratic Formula” (9-7) What is the “quadratic formula”? When and how do you use the quadratic formula?

Q. A quadratic equation is An equation with 1 solution An equation with 2 solutions An equation with 0 solutions An equation with 3 solutions.

Polynomial Inequalities 2.7. Definition of a Polynomial Inequality A polynomial inequality is any inequality that can be put in one of the forms f(x)

Quadratic Inequalities First day: Review inequalities on number lines. Review inequalities of linear equations Review inequalities of systems of linear.

The Quadratic Formula Quadratic Equation Quadratic Formula.

Chapter 4 Section 8. EXAMPLE 1 Solve an equation with two real solutions Solve x 2 + 3x = 2. x 2 + 3x = 2 Write original equation. x 2 + 3x – 2 = 0.

Warm-Up Exercises Write in vertex form. 1. ANSWER ( )2)2 x 3 + y 3 = + 2. Evaluate when,, and. 3 = a b 2b 2 4ac – 6 = b – 5 = c ANSWER 24 – ANSWER 25 (

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.

Solving Quadratic Equations by Graphing (9-2) Objective: Solve quadratic equations by graphing. Estimate solutions of quadratic equations by graphing.

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

TEST! Test on quadratic graphs! EXIT EXAM!!1 (3PM – 5PM)

Solving Inequalities Algebraically

Algebra 2 Test 1 Review Trivia

Warm Up Find the x-intercept of each function. 1. f(x) = –3x + 9

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

Notes Over 9.6 Quadratic Formula

5-1 Solving Quadratic Equations by Graphing and Factoring SWBAT

Consider the function f(x)= 2x2 + 8x – 7.

Using the Quadratic Formula

Transforming Quadratic Functions

Transforming Quadratic Functions

Warm Up HW: Quadratics Review Worksheet

Lesson 8-10 Nonlinear Systems

Solve Equations in Factored Form

Objectives Solve quadratic equations by graphing or factoring.

Quadratic Function model

Using the Quadratic Formula

The Quadratic Formula CA 19.0, 20.0.

Notes Over 9.5 Quadratic Formula

Use the discriminant to find the number of solutions

Solve a quadratic equation having two solutions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

LEARNING GOALS - LESSON 5.3 – DAY 1

Using the Quadratic Formula

Bell Quiz 3 The quantity is called the __________ of a quadratic equation. If it’s ___________ it has no real solution. Solve the equation.

Section Day 3 Solving

For example: f(x)=4x2+4x+1.

Presentation transcript:

For example: f(x)=6x2+17x-14

f(x)=0 f(2)=0 (2,0) f(5)=0 (5,0)

y= 6x 2 +17x-14 Factoring ax 2 +bx+c

x= 6 5

Zeros are x= 6 5 0=5 x 2 +4x-12 f( 6 5 )=5( 6 5 )2+4( 6 5 )-12 =5( 36 25 ) f( 6 5 )=12-12=0 We can check by substitution:

x= 6 5 x=-2

!

Rewrite f(x)= 8x 2 +18x+9 by factoring. What are the zeros of the quadratic function?

Sports. If you throw a softball into the air with an initial upward velocity of 38 ft./s. and an initial height of 5 ft. Use the vertical motion model h=-16t2+v0t+h0 to write an equation that give the ball’s height in feet at the time t in seconds.

b. The ball’s height is 0 ft. when it is on the ground b. The ball’s height is 0 ft. when it is on the ground. Solve the equation you wrote in part (a) for h=0 to find when the ball lands. c. How would graphing the quadratic equation help you understand the problem?

Error Analysis. Your friend attempted to solve the equation below Error Analysis. Your friend attempted to solve the equation below. Can you identify where your friend made a mistake? Now show the correct factorization and solutions of the equation. y=2x2-7x-4 y=2x(x+4)-(x+4) 0=(2x-1)(x+4) x= 1 2 and x=-4

Error Analysis (continued) Error Analysis (continued). What method would you choose to convince your friend that x= 1 2 and x=-4 are not the zeros of the function?