Using the Quadratic Formula Section 3.4 beginning on page 122.

Slides:

Advertisements

Similar presentations

EXAMPLE 5 Solve a vertical motion problem Juggling

Advertisements

Solving Quadratics Tutorial 11g Relating to the Real World Members of the science club launch a model rocket from ground level with a starting velocity.

HW: Pg. 287 #47-67eoo, 73, 75, 79, 81. ___________________, 5.6 The Quadratic Formula and the Discriminant _________. ______________, ____________________.

4.8 Quadratic Formula and Discriminant

Essential Question: What are some things the discriminate is used for?

4.8: Quadratic Formula HW: worksheet

Warm up – Solve by Taking Roots. Solving by the Quadratic Formula.

Solving Quadratic Equations – The Discriminant The Discriminant is the expression found under the radical symbol in the quadratic formula. Discriminant.

5.6 Quadratic Equations and Complex Numbers

4.8 – Use the Quadratic Formula and the Discriminant

5.6 Quadratic Formula & Discriminant

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

Holt Algebra The Quadratic Formula and the Discriminant Warm Up (Add to HW & Pass Back Papers) Evaluate for x =–2, y = 3, and z = – x 2 2.

3.8 Warm Up Write the function in vertex form (by completing the square) and identify the vertex. a. y = x² + 14x + 11 b. y = 2x² + 4x – 5 c. y = x² -

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.

Chapter 4 Section 8 Use the Quadratic Formula In this assignment, you will be able to... 1.Solve a quadratic equation by using the quadratic formula. 2.

4.8 Do Now: practice of 4.7 The area of a rectangle is 50. If the width is x and the length is x Solve for x by completing the square.

The Quadratic Formula & Discriminant Essential question – How do you solve a quadratic equation using the Quadratic Formula?

Pre-Calculus Lesson 5: Solving Quadratic Equations Factoring, quadratic formula, and discriminant.

Quadratic Formula You can use this formula to find the solutions(roots) to a quadratic equation. This formula can be broken up into 2 parts: b 2 – 4ac.

Solving Equations with the Quadratic Formula By completing the square once for the general equation a x 2 + b x + c = 0, you can develop a formula that.

 This is the part of the equation under the radical sign. (b 2 – 4ac)  When that is positive, there will be two answers.  When that is negative,

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

Notes Over 5.6 Quadratic Formula

4.8 “The Quadratic Formula” Steps: 1.Get the equation in the correct form. 2.Identify a, b, & c. 3.Plug numbers into the formula. 4.Solve, then simplify.

5.8 The Quadratic Formula Life is not measured by the number of breaths we take, but by the moments that take our breath away.

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?

Section 1.3 Quadratic Equations 1. 2 OBJECTIVE 1 3.

Bonus! Multiplying Binomials Factoring Solving By Factoring.

ANSWERS!. Completing the Square Level 1 Answers Completing the Square Level 2 Answers.

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.

ALGEBRA 1 SECTION 10.7 Interpret the Discriminant Big Idea: Determine the number of solutions to a quadratic equation. Essential Question: How do you use.

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?

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

Warm Up  1.) Write 15x 2 + 6x = 14x in standard form. (ax 2 + bx + c = 0)  2.) Evaluate b 2 – 4ac when a = 3, b = -6, and c = 5.

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.

-SOLVE QUADRATIC EQUATIONS. - USE THE DISCRIMINANT TO DESCRIBE THE ROOTS OF QUADRATIC EQUATIONS.

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.

How do I solve quadratic equations using Quadratic Formula?

Use the Quadratic Formula to solve 3x2 + 23x + 40 = 0.

Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 –

Solving by factoring & taking square roots

Solving Equations by Factoring

Warm-Up Solve by factoring:

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

Notes Over 9.6 Quadratic Formula

Solve Quadratic Equations by the Quadratic Formula

4.7 The Quadratic Formula Learning goals

Chapter 4: Quadratic Functions and Equations

Unit 6 Part 2 Test Review Algebra 1.

Use the Quadratic Formula and the Discriminant Lesson 1.8

Section 5.8 The Quadratic Formula

5.6 The Quadratic Formula and the Discriminant

4.8 The Quadratic Formula and the Discriminant

Unit 7 Day 4 the Quadratic Formula.

The Kinematics Equations (1D Equations of Motion)

Section 5.8 The Quadratic Formula

5.9 The Quadratic Formula 12/11/2013.

Warm Up Solve: (x – 4)(2x – 1) = 0 2. Solve: x² – 9x = 36.

Quadratic Formula & the Discriminant

5.6 Quadratic Formula & Discriminant

Notes Over 9.5 Quadratic Formula

3.4 – The Quadratic Formula

Using the Quadratic Formula to Solve Quadratic Equations

Solving Equations with the Quadratic Formula

Presentation transcript:

Using the Quadratic Formula Section 3.4 beginning on page 122

The Big Ideas The quadratic formula allows us to solve any quadratic equation once it is written in standard form. The discriminant is a part of the quadratic formula that tells us how many real solutions the equation has.

Examples -4 two imaginary0 one real4 two real

Modeling a Launched Object Example 6: A juggler tosses a ball into the air. The ball leaves the juggler’s hand 4 feet above the ground and has an initial vertical velocity of 30 feet per second. The juggler catches the ball when it falls back to a height of 3 feet. How long is the ball in the air? Reject the negative solution because the ball’s time in the air can not be negative. The ball is in the air for about 1.9 seconds.

Monitoring Progress

Answers