For

Slides:

Advertisements

Similar presentations

Solving Radical Equations and Inequalities 8-8

Advertisements

A-REI Solve equations and inequalities in one variable. 1. Solve quadratic equations in one variable.

Chapter 9: Quadratic Equations and Functions

EXAMPLE 5 Solve a vertical motion problem Juggling

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

Modeling with Quadratic Functions

Speed and Stopping Distances

5-8 T HE QUADRATIC F ORMULA Chapter 5 Quadratic Functions and Equations ©Tentinger.

Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – Find.

Objective Solve radical equations.

Copyright © Cengage Learning. All rights reserved.

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.

4-5 Solving Quadratic equations

The Quadratic Formula For any quadratic equation of the form The solutions are given by the formula:

9-4 Quadratic Equations and Projectiles

4.8 – Use the Quadratic Formula and the Discriminant

Section 2.6 Quadratic Functions. y = x 2 How many real zeros does it have? How many real zeros can a quadratic function have?

SECTION 3.4 POLYNOMIAL AND RATIONAL INEQUALITIES POLYNOMIAL AND RATIONAL INEQUALITIES.

REVISION What two parts make up the stopping distance of a vehicle?

Using the Quadratic Formula Section 3.4 beginning on page 122.

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.

2.4 Algebra 2cc Section 2.4 Solve quadratic equations by completing the square Note: you can’t solve x 2 + 6x + 2 = 0 by factoring or by square roots…

Solving Equations Containing First, we will look at solving these problems algebraically. Here is an example that we will do together using two different.

Notes Over 5.6 Quadratic Formula

Holt Algebra The Quadratic Formula. Holt Algebra The Quadratic Formula.

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

Section 1.3 Quadratic Equations 1. 2 OBJECTIVE 1 3.

Bonus! Multiplying Binomials Factoring Solving By Factoring.

Aim : How do we solve systems of equations graphically? Do Now: Graph both equations on the calculator y = x 2 – 3 y = x – 3 HW: p.236 # 4,6,8,10,12,14,60.

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.

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

Algebra 2 Standard Form of a Quadratic Function Lesson 4-2 Part 2.

MAT 150 Unit 2-2: Solving Quadratic Equations. Objectives  Solve quadratic equations using factoring  Solve quadratic equations graphically using the.

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.

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

Word Problems With Quadratics

You need two points to calculate slope.

Analyzing Polynomial Functions

Rule Time: Salute to Brakes! Scott Adamson, Ph.D.

Quadratic Equations Definitions:

Solving by factoring & taking square roots

Solving Equations by Factoring

HW: Worksheet Aim: How do we solve fractional equation?

Solving Rational Equations

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

Aim: How do we solve systems of equations graphically?

Notes Over 9.6 Quadratic Formula

4.7 The Quadratic Formula Learning goals

2nd period rd period th period th period

Chapter 4: Quadratic Functions and Equations

Unit 6 Part 2 Test Review Algebra 1.

Real World Questions with Parabolas

Solving Equations Containing

Warm Up: Solve by factoring .

Lesson 8-10 Nonlinear Systems

9-4 Quadratic Equations and Projectiles

Warm Up Evaluate for x =–2, y = 3, and z = –1. 1. x2 2. xyz 3. x2 – yz

9.6: Solving Polynomials when a > 1

Quadratic Function model

Solve by Graphing Solve by Factoring Complex Numbers Solve by

Which graph makes sense?

Notes Over 9.5 Quadratic Formula

Tough AP Physics 1 standard Question…

Algebra 2/Trigonometry Name: __________________________

DO NOW A video game company’s revenue is represented by the equation R = –12p2 + 400p where p is the price in dollars of the video game.

Example 1: Solving Equations Containing One Radical

Solving Radical Equations and Inequalities 8-8

Presentation transcript:

For 𝑦= −2(𝑥+1) 2 +4, what are the vertex , the axis of symmetry, the maximum or minimum value.

A ball is thrown vertically upward within an initial speed of 65 feet per second. The height h, in feet, above the starting point after t seconds is given by the equation h(t) = -16t2 + 65t. After how many seconds will the ball be back on the ground?

Your school sells yearbooks every spring Your school sells yearbooks every spring. The total profit p made depends on the amount x the school charges for each yearbook. The profit is modeled by the equation p = 2x2 + 70x + 520. What is the smallest amount in dollars the school can charge for a yearbook and make a profit of at least $1000?

Engineers can use the formula d = 0. 05s2 + 1 Engineers can use the formula d = 0.05s2 + 1.1s to estimate the minimum stopping distance d in feet for a vehicle traveling s miles per hour. a. If a car can stop after 65 feet, what is the fastest it could have been traveling when the driver put on the brakes? b. Reasoning Explain how you knew which of the two solutions from the Quadratic Formula to use. (Hint: Remember this is a real situation.)